I print on matte papers exclusively. Sounds like you are considering using art papers, not designed specifically for printing? That I don't do. I stick with matte papers designed for inkjet printers. Canson's Infinity line, for example, has a lot of variety and produces some great results.
But in general, printing on matte papers won't have the same dmax or saturation as with coated -- it is just a different beast. I specifically print on matte papers because I want the results they give me. For example, sure the colors aren't supersaturated, but wow are they soft, subtle and natural looking.
Matte inkjet papers are coated too. The problem isn't whether the paper is glossy, lustre or matte - it's easy enough to adjust gloss with spray, wax or other techniques once the print has been made, and, by doing so, you can increase the Dmax and colour saturation of a matte print to close to that of a glossy print. Put it behind glass (even museum-grade nonreflective glass) and the differences shrink even more. The problem is the inkjet layer itself - it's physically fragile and brittle (essentially being composed of a mixture of sand particles and polyvinyl alcohol binder in a roughly 10:6 ratio) and exposure to UV light and pollutants make it even more so. Pigments themselves may last forever, but that's no good if the layer they're printed on peels or disintegrates - a bit like how prints made a few decades ago on RC paper and kept in dark storage are now outlasting the RC layers they were printed on, or like how platinum prints, although 'indestructible', also catalyse the formation of acids in the paper on which they're printed, causing them to turn brittle and disintegrate.
I'm looking at using uncoated, but sized papers - Arches watercolour, Japanese washi, Indian khadi, some papers by Fabiano. Papers without a surface coating that can crack and peel, but also without a surface coating to facilitate the fast separation of pigment from carrier (to call them 'fast-drying' is a misnomer, since they don't actually dry fast - merely that the ink quickly flows through the microporous layer into the paper substrate, depositing the pigment in the layer as it passes through, so that the pigment is stuck there and no longer bleeds along with the liquid carrier - that's why these papers can outgas for 24 hours or so, as the carrier evaporates). Matte because they don't come in anything else (although you can adjust that later with sprays or wax) and smooth, for better Dmax and saturation.
There's really nothing fundamentally different about printing on uncoated vs coated papers using pigment inks, or any other surface, for that matter. The fundamentals are the same - the ink is low-viscosity so that it can fit through the nozzles on the printhead, the printer sprays it onto the print surface, and, to prevent pigments from spreading or bleeding (either horizontally along the paper surface, causing loss of definition, or vertically through the paper, causing loss of saturation) you need to quickly separate the pigment particles from the liquid carrier. After all, pigments which are no longer together with the carrier can't run or bleed - if you put it in a pen and try to write with it, pure carbon pigment in ink will run and bleed on uncoated paper, but the same pigment won't go anywhere if you apply it with a pencil or crayon. The only difference is that you've rejected one solution to this problem, and need to find another.
Microporous inkjet papers accomplish this separation mechanically - essentially, the microporous layer acts as a 'filter', allowing the liquid carrier to pass straight through, while trapping the pigment particles. But mechanical separation through a filter layer isn't the only way to separate solid pigment from liquid carrier. Evaporation also works - the faster the carrier evaporates, the less the ink can bleed. This depends on temperature, humidity, ink load and the composition of the carrier fluid. Temperature and humidity are easy to control - an inkjet print made at 15 degrees Celcius and 60% humidity will take a while to dry and look distinctly unsharp, but the same print made at 50 degrees Celcius and 20% humidity will dry a lot faster and be much sharper. Ink load can be controlled via the RIP but reducing the ink load also has the effect of reducing Dmax and saturation. You already need a greater ink load on uncoated paper vs coated paper to achieve the same saturation, since some of it will bleed down into the paper, rather than staying on the surface. Which is where heating the paper and ink comes in - at high temperatures, the ink will dry faster, leading to more pigment staying at the surface, and also allowing you to use a larger ink load for the same dot gain, which gives you an even deeper Dmax and saturation. Changing the carrier fluid is the most difficult to customise, and not really an option without some laboratory equipment (e.g. a centrifuge). Solvent vs aqueous inks are an obvious distinction between carrier fluids. But suspending the pigment particles in something like methanol (boiling point 64.7 degrees at sea level) or ethanol (boiling point 78 degrees at sea level) would lead to faster drying times and a sharper print/higher possible ink load, although you'd also have to find a way to keep the ink in suspension while it's in the printer, to avoid clogging. Increasing the pigment load in the ink, or increasing its viscosity, would also work, but would come with clogging problems.
As well as evaporation (already described) and mechanical filtration (already rejected), the other mechanism which can be exploited to separate carrier from pigment, and limit the movement of pigment particles once they have been printed, is adsorption. This is why dye inks don't bleed when printed on microporous surfaces (their longevity due to atmospheric pollutants is another story entirely). Rather than just being carried through the pores into the paper by the carrier, the negatively-charged dye particles are adsorbed to the fumed silica particles in the microporous layer, staying behind while the carrier fluid moves on. This is also how chromatography works, so it's not exactly a new concept. This can also work with encapsulated pigment inks, and is influenced by the composition of the external sizing of the paper. The more the encapsulated pigment sticks to the coating of the paper fibres, the less they will move or bleed. The resin coating on pigment particles in aqueous ink is hydrophobic/oleophilic - a surfactant keeps them in suspension in the ink - while aqueous liquid carriers are hydrophilic, which gives us a mechanism by which we can separate them via adsorption. External sizing used on non-inkjet paper (e.g. gelatin or styrene-acrylate emulsions) are designed to prevent water being absorbed into the paper fibres and the paper becoming soggy. It shouldn't be too difficult to modify this sizing with an additive that will increase the adsorption of resin-coated pigment particles to the coated fibres - already, calcium chloride is showing promise, and some major paper companies are working for bulk office paper. But, again, this requires custom paper (i.e. hiring the services of an independent paper maker willing to make specialty sheets in low volumes) and precludes bulk-buying of existing products in roll form, so it's not for everyone.
Naturally, I'm aiming to print on large sizes, as this minimises the loss of resolution due to the print process (a bit like how postcard-sized dye-sub-on-metal aluminium prints can look unsharp, but large prints look fantastic). An 8x10" or 6x18" print on uncoated paper may look horrible, but the same thing printed at 40x60" or 30x90" could look great. Call it the 'billboard effect', if you will.
I believe the future of printing on uncoated papers will likely be in a combination of modifications to printer design (e.g. preheaters, print heaters and dryers, as currently seen in solvent inkjets) and special uncoated papers with inkjet-receptive sizing, and that the currently-used inkjet-receptive coatings will become less popular for fine art printing, where durability is crucial, as their deficiencies become more apparent, just like RC-coated papers, which are also prone to cracking, and OBA-containing papers, which burn out and change colour, already have.
But, anyway, too much science and not enough printing...