I would say they work okish up to 50Mhz (FNIRSI more 25Mhz). 300Mhz not really. Like CDaniel mentioned, linearity is not really good.
I did some tests with a noise source over here:
https://www.eevblog.com/forum/testgear/test-equipment-anonymous-(tea)-group-therapy-thread/msg2416473/#msg2416473
https://www.eevblog.com/forum/testgear/test-equipment-anonymous-(tea)-group-therapy-thread/msg2860544/#msg2860544
Excellent analysis! Stable, repeatable, flat response is much more important than peak response.
That reported 300 MHz response could have been peakiness from a maladjusted probe. I found that when using the supplied X10 probe and playing with probe compensation, I could get my 1013D to display a reasonable representation of an 85 MHz sine wave.
a "sort of" related analogy:
With automobile engines peak H.P. of an engine is an interesting number--power generally happens briefly, just before you shift--but the level and flatness of the torque curve are much more important to real world performance on the street...
The original (1995) Honda S2000 delivered 247 H.P. @ 8600 RPM, but just 75 to 120 H.P. from 2500 to 5000 RPM, and barely able to launch itself from a stop. You had to "rev" it to 6 or 7 grand to get a respectable launch--whereupon everyone watching was wondering "WTF is wrong with that A-hole".
In the end it was just a plain ol' 150 H.P Jap 4-banger built to withstand 9000 RPM, and tuned to make the marketing people happy by producing an unusable horsepower "peak" at that engine speed. It was not at all a fun car to drive, which is the whole point of "sports cars".
The best description I ever saw was that "it is a great car as long as you drive it like you just stole it."
My point is that examining only a single characteristic of anything (oscilloscope probes, automobiles, or elephants) will earn you just a singular and partial perception of it's value and utility.