This is very much my experience with the 55-250mm STM as well. Cheap and amazing. So sharp that I thought I got lucky with MFA on my lens-body combination, but then it was just as sharp on my new body.

A 70-200 L lens with stabilization would cost at least 7x as much as a 55-250 STM, and, in my opinion, would offer no tangible advantage for shooting airliners for screened sites. If you're looking at Canon, save your money and squeeze as many megapixels as you can afford out of a used two or three digit DSLR.