The way I see it is that it could only actually collapse if the electron was headed precisely at the nucleus (the nucleus has diameter zero in this simplified model). Even in classical physics, the electron would move on an ellipsis around the nucleus in almost all cases, so the average distance would be non-zero.
Being pointed exactly at the nucleus is not possible in quantum mechanics, because that would require infinite precision, which is precisely what we give up in this model, so the average distance is yet again non-zero.
This explanation is not correct. Here, the electron is again accelerating, will lose energy, and ultimately spiral into the nucleus. This does not require it to be pointing exactly into the nucleus.
Being pointed exactly at the nucleus is not possible in quantum mechanics, because that would require infinite precision, which is precisely what we give up in this model, so the average distance is yet again non-zero.