I think it more has to do with his hunger (Or lack thereof).
Nasty Nas was pretty much killing his features back in the day (Like his Live at the Barbeque verse), and then dropped Illmatic. Because back then, he had something to prove. Just like the Eminem that was on Renegade that killed Jay, or the 50 cent that was on Power of the dollar/Guess who's back. When you're hungry and determined you will do things that you've never thought that you can do. It brings out the aboslute best
But over time, as you get more comfortable and that hunger fades, you become more complacent, or even lazier. Unless something happens that will revitalise you...you'll either just remain at a particular level (Like Nas) or you'll fall off (Like 50).
To me Nas is just as dope a lyricist as he was back then. Only now he' isn't as hungry, as he was before.
This isn't unique to only artists though, this is life in general. As time goes by you become less and less the monster you were in your prime.
Of course. But still...Rakim is respected for his sheer talent in lyrcism, and was the dude that raised the bar in terms of the MC's pen game.
Well for starters, I just want to point out that it's not as black and white as "Non-lyrical rappers being more appreciated". A lot of non lyrical rappers suck major a$$ too, and are rightfully shytted on. (Soulja Boy, Lil B and so on)
Then there is the fact that now there is more of a formula as to what will get you put on. It's not so much about how well you can rap anymore, but more or less who good a club anthem you can make. Mainstream hip-hop is mostly comprised of club anthems and "Whip-music" (As you Americans would say), you don't really have to be lyrical to make a club anthem. You just need a catchy chorus and a catchy beat.... while rap songs of any other kind of subject matter, or any decent level of lyricism are relgated to the underground, so you would have to search for those.
You should also note that, lyrical rappers are appreciated, even nowadays. Look at the love the Kendrick is getting for his album. Guys like Sykzoo have fans (Too bad he'll never get that big break

)
I think you question is not so much "Why are lyrical rappers not appreciated", but "why aren't they as popular as before in the mainstream", and well I would just say that's the consequence of any musical genre that gets popular and money gets involved. Sooner or later businessmen come up with a formula to make money and the artform is affected as a result. The gimmicky cash grabs rise to the top and everyone else falls to the way-side.
Anyways, back to my original point...you can make good music whether or not you're lyrical or not. Rap is music, so no matter what style you use, if you're original and your songs have some kind of meaning then you're gonna be dope regardless of how lyrical you are...Pac and Nas are good examples of this...both dudes on either side of the fence in terms of rapping technique that both managed to create classic material.