I have wondered this about some as well, actually. One poster on the primary NYCFC Forum against it has a picture of Klopp as his avatar, and of course those two clubs have a larger following in the U.S....for now.
I suspect it is also a NYC and American sport fan thing as well with regards to the impact of MLS being inferior (which it obviously is) when us Yanks are so used to having so-called "top" players in our most popular sport leagues. The idea of being "2nd fiddle" doesn't go over well with certain types, and is partially why some fans want younger players, or players who are supposedly "more hungry" to play in MLS to prove themselves, at least, to use with the "DP" (Designated Player) contract (a limited number of highly paid players, given "salary cap" restrictions on others). One problem is one player many want, from Atlanta (Almiron) could very well go to Europe in the next transfer window.
The issue with MCFC not loaning many talent to this point, other than Angelino (whose poor performance/experience I suspect led us to be more careful about loans to NYCFC since then), has not been utilised much, and adds to this feeling.
I'm an NYCFC supporter, although more casually, but naturally as I am of course an MCFC fan from and live in NYC. I am 100% in support of Yaya coming to NYCFC and think he would do very well as they are in need of a play maker, more attacking nous, and I think his ability to keep the ball in tight spaces will be effective even if he is under heavy pressure, which we know Yaya can thrive under. Under Vieira I think he will keep up his effort levels as he will respect him as manager (assuming he is there next season, which I expect), also being Francophones of African descent, and I suspect like to see Vieira succeed given Yaya's outspoken nature about racial justice issues, and that we have yet to see a black manager reach top levels of the game, which Vieira is certainly considered one of the best candidates. To me, Yaya dropped his last two seasons under Pellegrini, particularly the last being a lame duck manager with a soft touch that helped following Mancini's abrasiveness, but I don't think he was alone (see Kolarov vs. Southampton).