This is only a problem because it's the singer. Vocals and melody are the most recognizable and easy-to-process part about a song for the average fan. It's also the easiest thing for the average fan to notice that there is a difference. No one is going to pass Chester off as Scott. However, the average fan--read: the vast majority of fans--will not notice a huge difference if one of the other guys was replaced.
This is why the Van Halen equivalent of this board to this day has nasty Sam vs Dave threads, but Van Halen still sells out shows despite Eddie's son playing bass, not Michael Anthony. This is why Pearl Jam goes strong and no one really cares that Pearl Jam has gone through 4 drummers.
To me, for example, "Given to Fly" is unlistenable with Matt Cameron on drums. To me, for example, the last Van Halen album sounds equally Van Halen and Dave solo because the bass playing is different and there is no Michael Anthony on backing vocals.
But there are some people who aren't just the average fan. I play an instrument. I have recorded somewhat professionally. I have friends making a living as musicians. I listen to music differently--only because I have trained and practiced. In many cases, there is a big difference when even a drummer, bass player, or guitar player is replaced. Yet the vast majority of fans never have a huge problem when that happens--only the singer.
Yes, sometimes certain personalities dominate a band. Eddie Vedder is a great example. But even in the case of Pearl Jam there is a world of difference in their drummers. They've made no attempts to hire drummers that bared any resemblance to the previous drummer. And it makes a big difference. Perhaps it's not as big a difference for most fans, but it's enough to make it tough to listen to Matt Cameron play stuff from before he was in the band, at least for me.
Obviously, in a perfect world, previous STP fans would prefer a healthy Scott leading the band. But since that isn't happening, the rest of the guys got a new singer. It isn't new in rock and roll. Sometimes it works, like Van Halen. Sometimes it doesn't, like Bad Company. This was not an artistic decision. The decision to continue the STP name serves the financial interests of the band, is probably a reason Chester even agreed to do this--STP is one of his favorite bands--and it also servers to show that, at least for now, the guys are done with Scott.