DY:
I suppose that who possess an IQ on the positive side of 0 understand that each kid facing expulsion by a yeshiva is an individual case to be judged on its own merits. What makes this worth discussion is that it is commonplace for yeshivos to throw kids out impulsively. Whereas there must be those who have faculty meetings where they discuss the matter, there are certainly many that do not. Sorry, no statistics. I have heard many, many cases where a kid is simply ejected, for him and his parents to fend for themselves. In certain cases, these yeshivos were corrupt enough to call other possible yeshivos where the expelled talmid might go and warn them to not accept him. Not as a rule, but not a rare exception either.
The pikuach nefesh factor seems to be ignored, and the role the yeshiva should be taking to work with the talmid (albeit a challenging one) is also bypassed. The Gedolim of yesteryear were highly opposed to such practice, though using this as an argument to stop an expulsion has not worked.
I agree that there are yeshivos that cannot work for certain talmidim, and they need to go elsewhere. An earlier comment noted that “throwing out” must be accompanied by finding an alternative placement. I agree, but optimism here is hard to find.