Some change of scenery is also nice at some times. But like the previous answer already said, I don't think players at age +30 are still considered really that high caliber players in Europe. (Except the exceptional players off course.)
But I also think if club owners can sell those players the idea of promoting the MLS, helping to grow it, they would be interested in such a case. Football isn't nearly as popular in the US as compared to the rest of the world. A lot of players are egocentric enough that the would think, well I want to help to change that.
But I don't know if that's the case for players like Gerrard. He's still playing at a high enough level to already quit, but
- he's too old to move to another European club/Too expensive
- Doesn't probably want to play at another Premier League club to not disrespect Liverpool
So, he has limited options.
Also it's extremely difficult to compare statistics between the European leagues and MLS.
Salary is a bit of a non-factor I'm afraid. Medium teams all around Europe can offer the same wages as MLS clubs. So if a high caliber player is good enough for Europe, he's going to Europe. That's why South-Americans go to Europe. The same amount of money, but they're playing in Europe. Much closer by the big competitions like Bundesliga, Premier League. You've got the Portugese and Dutch competitions that have good reputations to "prepare" players for the next step. They play at the top in those competitions, show them at European games to reach their dreams maybe and play for Bayern, Barcelona or Man Utd. That's what's pulling them toward Europe.
MLS is one competition that's static (I mean no relegation/promotion) which is a really big factor in European football. That might be something they should look into. Two (or more) connected divisions, that would maybe make football more popular in the US, more spread around the country as to 20 teams now. If it's popular, there are higher attendances, there is more income, you get more money => better competition + more money = better players => start the last sentence over (and over, and over, ...)
It has come already a long way the MLS, given its rather short length.
The thing that they've got going for them is I think the overall accommodation. It's all newer, brighter, shinier than some of the old stadiums over here(while we still love thos :) ), the US is at the top of the world for that. And that could be an important factor in the future growth of the MLS. But you don't need the exceptional European players to become a big competition I reckon. If you don't need them for the NFL, NHL, NBA, MLB. Why so for football? Invest in the youth is my advice ;)