I don't think it would crush airlines from a cost point of view. Remember that the TSA is not free now, and we are paying for it through other means.

As it stands, TSA is paid for by taxes (from both airlines and consumers).

In the privatized scenario, airline companies and consumers pay less in taxes, ticket prices increase to pay for private security.

You could call it a wash in the worst case, but in reality it would likely end up as a net gain to society because privatization has a strong history of cost savings over government solutions:
http://en.wikipedia.org/wiki/Privatization#Pro-privatisation

Regarding what you said about "they simply implement the policies regulators impose" - this isn't full privatization of course. In the scenario I'm imagining each airline would have the freedom to chose their own policies and there aren't regulators.

Finally, just wanted to look at what you said about a focus on maximizing returns leading to a disaster. This is the counterintuitive argument and greatest discovery of capitalism in my mind - that a selfish focus on maximizing your own benefit can actually lead to the greatest benefit for society as well.

Think about how an airline would actually maximize their returns. They'd probably need to get more customers right? To do that they'd have to convince customers they provided the best product at the best price. Customers aren't dumb. You couldn't just provide "security theater" that had little actual benefit, customers would call your bluff. So you'd have to actually convince them you were doing a better job for the cost. What I'm getting at is that maximizing returns is the most honest way we've ever devised to get real results - either you're doing a good job (and people let you know by giving you their hard earned dollars) or you aren't and your company is unapologetically weeded out (bankruptcy, acquisition, new management). It's a lot like natural selection.

Yes, at some point there will probably be an airline who makes the mistake of using short term thinking - (cutbacks on security which aren't apparent at first but lead to a disaster). But this is a self correcting problem in that if it comes back to bite them their business will likely be sued out of existence. (You can't say the same for the TSA.) It's unlikely to happen often though. I think in the same way you trust a Mercedes over some brand new car company who is only focused on short term thinking, customers would buy tickets from airline companies they trust with long track records. This is another way of saying the market rewards long term thinking companies when appropriate.

Naturally, some companies will spend less on security and offer cheaper tickets - this is actually a good thing - it segments the market for people based on their risk tolerance. If you think the whole thing is overblown and know the real risks (as someone mentioned above you are more likely to be shot by your neighborhood police officer then die from terrorism) you get cheaper tickets!

Anyway, this is a long winded explanation, but the gist is that free market competition has been shown to produce better results in areas like this. I'm perfectly willing to admit it doesn't work in all cases. I just haven't heard or thought of a good reason why it wouldn't work here yet.