So is a higher ink density usually better or does it vary with the paper?
From my understanding you're thinking on this is in the wrong direction. Some papers can take more ink without issues, while others can only take smaller amounts of ink. Thus the need for ink limits. For instance many of the photographic style papers, such as Baryta or Canson's Platine can perform very well with higher density, while a mat style paper might require medium density.
I was surprised lately to find out the Breathing Color Crystalline Canvas has a media configuration via Breather Color of only a low density. I built my profile using their MCT file which resulted in an excellent profile for my Pro 4100 printer. At the time I would have thought this canvas would have had more similarities to a Baryta, Gloss or Satin type of paper.
At the end of the day, what it boils down to is, how much ink can a particular coating on a particular type of paper take on and absorb. Understand too laying down too much ink will NOT make for better and deeper blacks and in fact just the opposite can occur if those darkest values are loaded with too much ink, but you also don't want to starve those values of enough ink. Thus the need for linearization, which the ink limit/density within the MCT tool accommodates albeit in a rather crude manner.
Hope this helps.