With so many people saying Steve's Kermit and Ernie are the ones they grew up with, I grew up with an interesting combination of both his and Jim's versions.
I was born a year before Jim died, so Steve was already performing the characters by the time I would be old enough to remember, well, anything. That being said, however, as a tot, I already been seein Jim's versions of the characters through home video: I had a number of My Sesame Street Home Video tapes with clips and inserts of Jim's Ernie and Kermit, not to mention we had movies like TMM, GMC, MTM, and FTB on VHS, so I was very well familiar with Jim's Kermit and Ernie when I was a little kid . . . I don't think I even knew that Jim was dead or that Ernie and/or Kermit had been recast until MTI came out in theaters, but I guess I didn't think much of it because I don't remember Steve's Kermit phasing me when I saw MTI - I guess because at that age, I already knew how to accept such things: when SPACE JAM came out, I was aware that Mel Blanc was dead, and therefore, the Looney Tunes would have different voices, so yeah.
Not to mention, I think we all here know all too well that while the Muppet characters may go on forever, their performers don't, and we just have to accept it when they get new performers: they may not sound or act exactly the same, but if they did, that would be nothing more than an imitation, and the performers need time to bring something from themselves into the characters, like Steve did with Kermit and Ernie; they're not Jim's Kermit and Ernie, but that doesn't make them better or worse, just different. Same with Eric doing Frank's characters, or Matt doing Jerry's characters, or David doing Richard's characters - we all have to make adjustments, but as long as people are willing to keep these characters alive, that's what's really important.
Having said that, until we hear something else otherwise, my conclusions about this are that either Disney fired Steve for butting heads with them to much, or Steve left the Muppets for similar reasons Joey left SST.