Plenty of schools say they allow transfers to do "OCI". The problem arises when Phase I of OCI (the only phase that matters) is not available to transfers.
"Phase I" being bidding? I think you need to recheck your facts, man. Allowing transfers to put in bid lists is definitely the norm.
First round of interviews, which generally takes place in August before classes start, and often before transfers know they are attending that particular school.
First rounds are usually like mid-late August for many schools, IIRC. Transfers should be prepared for OCI before getting admitted, however, especially if decisions don't come out until near the deadline for bidding. Moreover, since most schools do rolling admissions, it's really on the applicant to get applications done early/ready to go when grades come out (again, the exception being schools that don't release grades until really late, etc.) and thereby maximize the possibility of hearing back sooner. Thus, the transfer applicant should be doing preemptive work both before applying and being admitted.
To be sure, some schools continue to admit students after their bidding deadlines. Some schools, however, give transfers a "special" extended bidding deadline. For schools that do not, students should take that into consideration before transferring. It's on the applicant to weigh the pros and cons of such a situation (IMO, probably not worth it).
Re transfer OCI and timing: if you're transferring to take advantage of OCI, you should already have all your shit ready to roll before transferring (e.g. cover letter templates, resume, references, etc.). Moreover, transfers should be prepared to put in LOTS of work in firm research, writing targeted cover letters, etc., in getting ready for OCI...even if that means spending days/nights in front of the computer.