No the 10% 90% is because you can't possibly accurately tell where exactly that edge begins and ends. If you want to cheat the rise time then you define it as 20% to 80% (some do use this trick)
Getting bandwidth from rise time is also not always completely accurate because it depends on what shape the frequency response has at the cutoff point. But the shapes that optimize a faster rise time out of the same bandwidth will also generally have more overshoot and ringing. Still the resulting bandwidth number is going to be about in the ballpark of +/- 20% so its good enough.
As people have said square waves are better for testing oscilloscopes because it not only shows the approximate bandwidth but also shows if the cutoff response of the input introduces extra overshoot. A lot of scopes will have a little bit of overshoot and that is fine, but if the overshoot is something like 20% of the signal amplitude there is definitely something wrong.
As a source for generating these fast rise time square waves its easiest to use a fast digital logic chip driving the coax trough a 50 Ohm termination. One popular circuit for doing this uses parallel Hex inverters
https://www.epanorama.net/circuits/tdr.html to produce a fast clean square wave (Typically used for TDR measurements of cables, but is also an excellent oscilloscope test signal)
