You're probably as tired of hearing this answer as everyone else is: it depends.
"Cost-effective" can mean an awful lot of things. As you've stated it, it's all about the post-processing — but is it really? If you're working at the lower end of the market, your dollar is coming primarily from getting faces in front of the camera. Turn-around matters, but not mearly as much as getting people into the studio if the image turn-around is reasonable. Frankly, a lot of that market isn't about getting that one perfect image, it's about catching people on a whim before they change their minds. Does anyone really need to be on the cover of an ersatz outdoor life magazine or a baseball card? Probably not, but if you can get them to buy into stardom in addition to the ordinary portrait session, you're ahead of the game. What happens when the client decides later that the background doesn't go with her blouse? You've got the session fee, but you've lost the prints (or whatever your final product is). A proofing site that allows background swaps before print orders can do a lot of this sort of marketing for you. And are you missing out if you can't offer the fun impulse picture?
At the very high end, the post-processing is going to be extensive in any case. This isn't the stratum where a couple of clicks in Portraiture or Image Doctor will get you where you want to go — a beauty shot, whether for advertising or editorial, can often be a full day's work in post. I don't know if chromakey is where you want to be here (colour bleeds and specular reflections can be tricky sometimes) but masking and compositing can certainly come into play. (I like to point to the work of Joel Grimes, among others, at this level.) Here, you may be putting the subject very much into an environmental context, but with the full benefit of studio lighting for the subject and the best possible composition and exposure for the environment. Even in a context-free setting (seamless, for instance), you get to play with the colour, tonality and gradient afterwards, and an easily-masked white, back, or neutral backdrop can give you (and an art director, if one happens to be involved) a lot of options.
It's that bit in the middle-to-high end, where the client is paying a premium for a good studio portrait (or headshot) that is supposed to look exactly like what it is where there's not much real gain. Your subjects are going to want the "studio look", whether that means a mottled backdrop (bleh!), an obviously fake scenic (again, bleh!), a neutral gradient, or what have you. You can easily get away with a couple of backdrops and a couple of go-to lighting recipes.
Don't forget the "nuclear option", though — if you're working at near-capacity, and post-processing turn-around after image selection is getting to be a problem, then there's a pretty good chance that you're wasting your valuable time. It may be time to hire or outsource so that you can stay in the studio and make the "big bucks" while someone else sweats the small stuff. Time in the studio is making money; time in post is spending it. If you're charging, say, $100/hr for your time in studio (that's nowhere near the high end) and can book an extra five or six hours a week by handing off post, that's a 20 hr/week employee paid for. The more you can gain in shooting by offloading processing (and, obviously, the more you charge in session fees) the better that gets, and the extra couple of minutes per image doesn't mean nearly as much when it's costing you so much less. (And keep in mind that at the client proofing/ordering level, the work doesn't have to be immaculate — just good enough for the web page or contact sheet. The heavy lifting can happen once the order is placed.)
