Having some sort of covering (i.e. large plastic bag) is reasonable. Non cyclists don't want their luggage covered with road dirt and chain oil.
My first flying trip was the easiest, just turned the handlebars sideways, took the pedals off and handed the bike across (Glasgow).
Since then I've tended to use the CTC bike bag and ride away from the airport, though my habit of flying in padded shorts may have to change...
I was told Nice airport had a bike assembly area and tools, but I've never used them, though I've flown back from there 3 times.
For the US trip I used the S&S couplings on the bike and packed it into the S&S soft case. I assembled the bike at the hotel and posted the rolled up case to my hotel in SF.