I think 1/2 is a bit generous. iirc, about 1/4th when I did a multi year exploration once. But many of those are actually decorated military veterans which are somewhat increasing in last years. They have a little sumthin sumthin that an average stellar PTK transfer applicant doesn’t have. The rest are from Ivy level colleges, unusual backgrounds of high national/international accomplishment, and some 4 years that have distinguished themselves in a particular field and that target school has expertise/libraries/profs they need.
If you mean HYSM you should say so. You named 5 colleges and one doesn’t take transfers. Two to four take 25 give or take a couple. um, yeah, bad odds.
Also I think @menloparkmom meant Cornell, which takes a lot of transfers, not Columbia College which doesn’t take many, however Columbia GS does.
Many students with an AA via dual enrollment/early college will apply as freshman. That is the optimal path.