"Because it is an unnecessary inconvenience and it makes me look bad to my clients"
No. As someone who manages a fair number of domains through BR, what makes it look as if you were not doing your job is the fact that you failed to read the notices at the BR site about transfers to Enom. If you had, you would have known that you need to get in touch with BR first to confirm an Enom transfer.
"totally discriminatory and unreasonable policy"
Not at all. I imagine things have improved, and I'm familiar with folks at Enom, but the simple fact is that there was a very, very large numbers of domain names that were hi-jacked a while ago through Enom. This was quite a while ago, but I can remember when it seemed like I was getting about a call every other day for a month, in which someone was complaining about their domain name being the subject of an unauthorized transfer to Enom.
Under the current transfer policy, the losing registrar can deny a transfer to the gaining registrar if the losing registrar reasonably believes that the gaining registrar uses an inadequate confirmation mechanism.
BR made a perfectly reasonable decision to nack transfers to Enom, instead of tying up their entire support staff 24/7 to deal with the volume of unauthorized transfer that were being sent to Enom.