I've had TSA search my bike I brought on board probably 3/4 of the time. Few things I've noticed:
-Steel Ritchey Breakaway almost always has the TSA open the luggage it's in, look through it without messing anything up, leaves a note saying they inspected it. Let's face it, on X-Ray it looks like a bag of pipe bombs.
-Full Suspension Mountain Bike - I don't think they've ever opened the checked luggage. Almost always they separately search my carry-on which ends up containing the rear swingarm and crankset/pedals of my current mountain bike. I take those separately from my checked luggage as I'm afraid to put my carbon swingarm in my luggage, probably over cautious. I tend to take crankset/pedals in my carry-on as they weigh a lot and helps keep under the 50 lb limit.
-Newark doesn't search anything. All anyone cares about at Newark is luggage is under 50lbs.
I've got 10+ trips with a bike in checked luggage in basically standard sized luggage. Biggest issue is staying under the weight limits, nobody ever pulls out a tape measure. I always say bike PARTS and my CLOTHES. My luggage (Ritchey Breakaway bag lately) zips open and reveals pretty much the entire contents. TSA just needs to unzip, open the flap, see there's nothing to worry about, zip it back up. My fear with some of the other bags like the BikeNinja is you need to pretty much pull out the contents to see what it is.
One of the biggest reasons to go with BikeFlights is if you can ship it out early for your trip, you'll know if it arrives safely. I nearly have a heart attack every time I'm at the airport at the carousel waiting for my bike to come out.
Southwest doesn't charge for carry-ons. I have a United credit card so my checked baggage is free. So I don't think I have paid for taking a bike with me on a trip yet. Just the time to disassemble/reassemble. Which I don't find to be a big deal as it provides an opportunity to do maintenance.