Forgive me for being new,but ...
Wouldn't the way the ink reacts with the paper differ from supplier to supplier? Thickness, opacity, levels of pigments or whatever, are all different (I used to work for a major print company some years ago)
If so, the canned profile will work better for some printers than others.
Rolling your own should take these variations into account (along with batch to batch variations).
In a word, No.
Any profile, canned or not, is a paper/printer(ink) profile.
So even the canned profiles are specific for the paper/printer combination.
Some paper manufacturers have historically made fairly poor profiles but in general the standard has improved greatly.
(Also printers themselves are also much more consistent model-to-model so variations there are much smaller - perhaps even non-existant.)
So, depending on the paper/printer combination that one uses a custom profile may be the way to go or the canned profile may be as good as any custom profile.