Yeah, there are only 3 stats that upgrade directly via Crystarium which are HP, Strength and Magic. All of them can be boosted via weapon/armor upgrading (HP's a little harder of course, but still doable), so if for whatever reason you find your current Crystarium levels insufficient with the cap, there's still a way to improve your characters beyond their statistical level equivalents. And you can definitely grind to boost them since just about everything gives refinable materials, and if they give shitty ones, you sell those and buy better ones from various shops. The option of grinding still exists, yeah, just not in the "lol OVERLEVEL!" way.
And...that's a good point, Snowfire, hadn't thought of that! I'm not sure if that's the thought put into FF13's Crystarium as far as level caps go, but the Crystarium in general definitely promotes flexible set ups over specified ones. After all, there's a clear advantage to raising all 3 of the primary roles vs. one if only because stat gains are evenly divided that way (I know when I first started, I figured "ok, Ravager will raise Lightning's Magic, Strength through Commando! Became soon apparent that this is very much NOT true, as stats are just sort of shoved around all over the place, and you definitely want to raise all 3.)
The specializing aspect only really kicks in for skills (someone who rarely uses, say, Ravager will have no reason to branch off and waste CP on Ravager skills. This is actually a fair and legit decision. The stats of course are always useful, and generally skills are at the end of Paths, so skipping on skills rarely hurts your stats, thankfully) and when the full roles open up. Still, yeah, game definitely wants you to at least invest in the primary 3 roles.
(This isn't me challenging your point, more just reflecting on it. The only thing I "question" is if Specializing had anything to do with Crystarium Cap.)