The professional benefits of an MFA from a respected but not 'famous' program may be subtle but they're real. If your MFA is from Yale (or BFA from Julliard!) they're NOT subtle, I'm sure. I imagine that doors swing open. But, if your MFA is from a not broadly-known program which nonetheless provides solid training (which may be flagged on your resume by corroborating experience, skills such as stage combat or singing, and names of coaches respected in the field), then you may have to try the doorknobs to find out that doors which appear closed are at least unlocked and swing easily inward if you knock. Without my MFA, I would not be getting many audition appointments I seek out, and theaters such as The Folger or New Jersey Shakespeare Theater would not be calling me back to ask is I have local housing or need to be put up. Granted, I have solid theater credits on my resume, but those credits are there because I have the training, too.
My moral is this: an MFA is not just for teaching (though those kind of MFAs do exist. E.g., an MFA from a pedagogy-heavy program such as Texas Tech is not a good idea if you hope to work as an actor, rather than as a teacher--casting directors will see the slightness of actual training show up in the experience and details on the resume--but they're good for teaching at many universities and even more high schools.) An MFA from a strong conservatory-style program is a strong indicator that an actor can do the job on stage.
However, critics of the MFA do have a point: they say it's oversold on the mistaken premise that it will secure an actor paying work. Nope. It will not secure work. An MFA for anything other than a teaching credential is not a good business investment. It is, however, an excellent artistic investment. It's intensive training that is difficult to replicate elsewhere, on an ad hoc basis (I hasten to add that solid conservatory training does exist for people without college degrees--e.g., The Atlantic Theatre Co. School--so that it's not the MFA per se, but the training it represents, that I'm defending. For those with a bachelors degree, however, an MFA can be the fastest road to excellent training.)
So far, my MFA is doing everything for me that I can fairly ask of it. It isn't doing that on its own, however, just by virtue of being on my resume. It's doing it because I spend a lot of time trying door knobs that look un-openable, at first glance. I pound a lot of pavement, but that pavement would be wasted miles, without my MFA.