Yep, you keep digging that hole "Fungus"
What hole?
In practice brick wall filters cannot be achieved in hardware, they have to be done in software.
This means that if you want a 'scope with a a non-gaussian filter you have to sample at a much higher rate than Nyquist then digitally post-process it.
ie. you have to massively underrate the bandwidth which is printed on the front - inside the oscilloscope it has to actually have the bandwidth needed to match the sample rate.
In other words, it's a bit of a con game played in "high-end" oscilloscopes. That Tek paper which was posted earlier is really just a sales brochure in disguise ("You want a 'scope with only 3% error in rise time instead of 30%? We sell those!").
The reality is that a 'scope with 3% error is just a scope with 30% error (ie. gaussian filter) that's been derated, has a software filter applied internally, and a different label stuck on the front.
If you want to believe those scopes are breaking math, well... that's up to you.
I tell you what, why don't you write to Tektronix/Keysight and tell them how they have it all wrong, and you know, for a fact, that it's all a big conspiracy to sell more high end oscilloscopes. Let is know how you get on
Incidentally I didn't "massively underrate" the bandwidth that is printed on the front, in fact I specifically stated "The oscilloscope can (and probably will) continue to display signals way above the quoted bandwidth."
Like I said, the difference between the actual, calculated, and archaic theoretical rise time is probably a moot point for most people, and I doubt many people here would have the actual capacity to accurately measure the rise time of a fast oscilloscope in any case. However the point is that the rise time may be of significance for some people in their applications and they may specifically seek that when looking for their test instrument. It is incorrect to assume all oscilloscopes of the same bandwidth will have the same rise time. Tektronix say that. Agilent say that. Keysight say that. In fact the only person who seems to not be saying that is you
In practice the solution if the rise time is too slow is simply to get a higher bandwidth oscilloscope. However one shouldn't assume a specific rise time based merely on quoted bandwidth, as that is not always a correct assumption.
BTW my background was largely in RF, and I'm offering this emoji to the assertion that filtering
needs to be done in software