There’s actually less specialized parts these days, that’s what put Lego in trouble in the 90s, I think what GP commenter was referring to is a ton of the studs and cylinders and 1x1 diagonal parts that Lego includes, that are “fluff”. These parts are extremely cheap to produce, so you may have data that looks like price per part is flat, but in reality that’s because more of your sets are now from cheaper detailing parts.
having collected through the 90's, I can attest that there are a lot less specialty parts now, but in recent sets that number appears to be growing again. almost every fairly large set I've purchased in the last 2 years have had 10-12 new-to-me parts in it, and the other sets continue to include those same parts as well.
mostly, they've been pieces to make some change for SNOT, but there seem to be so many of them now that it feels like we're going back to that 90's mentality.
some of those sets:
* batman shadow box (with my first ever missing piece!)
* dune ornithopter (great build)
* loop rollercoaster (not counting those loop tracks)
* orient express (my least favorite build in the last few years)
I'd say yes and no. I find very few parts that are custom shapes for a single set these days. Most part shapes are very generic, but there is an absolutely wild variety of them now. There is an enormous number of SNOT, tile and slope pieces, for example. These can make slick looking builds, but getting a decent and useful collection of those for MOCs is hard.
Where Lego gets tricky is the combination of shape and color: the color palette has been growing over the years, too, but most of the weirder shapes are only available in specific colors and not always the colors you would intuitively expect them to have. I guess it happens because manufacturing/stockpiling the whole outer product of shape x color is just infeasible at this point. So the available colors are just whatever is used in the current sets, however weird it may seem.
Do you have some example? My kid uses "popcorn" parts to make chimney smoke, he uses "wolfverine claws" to make thatch roofs. Yes there are more parts created all the time, but you can still use them in very creative ways.
Makes me sad for the kids - this limits creativity...