You can circumvent using pre-processed data by choosing the timebase so that the actual samples are used for a measurement.
If I understand what you wrote correctly, a long record length would make this worse. Won't that be a marvelous opportunity for marketing to advertise their shorter record lengths and lower sample rates which will allow accurate RMS measurements to be made.
Or they could just fix it. It is not like we have not known how to make reliable RMS measurements on DSOs (and sampling instruments) for decades.
Besides that many DSOs have FFT which could tell you something about the frequency spectrum of the noise as well.
This would be more useful if one could take for granted that DSO FFT functions worked to make absolute quantitative noise measurements. Almost all fail and offhand I do not know of any which work correctly. This
EDN article discusses the problem.
I do not have any DSOs with an FFT function that I trust for this so at low frequencies, I use a 7A22 to make absolute RMS spot noise measurements. Then with some math I can usually derive the 1/f noise corner frequency. None of the budget DSOs I have tested could make this measurement with their FFT function.
When doing differential measurements using 2 channels I always had more trouble to get the vertical range setup in a way I still got some visible signal without overdriving the input.
That is definitely a problem and one of the reasons that better oscilloscopes place the overdrive limit outside of the visible display. One of the tricks to getting good results on an analog oscilloscope is to use the variable function on one channel to exactly match the gain of both channels; to me it is eerie to see the visible noise suddenly decrease to a minimum when CMRR (common mode rejection ratio) is maximized.
Also DSOs have averaging, hi-res or (even better) input filtering which cleans up noise from a signal nicely.
Averaging and high resolution acquisition mode are very powerful functions. Input filtering is common on all oscilloscopes to one extent or another.
Nowadays a Tektronix TDS500 or TDS700 series is a good choice if you want a compact 500MHz DSO for relatively little money. The service manuals including schematics are available and many people know how to repair these.
The only service manual schematics I am aware of are for the old TDS series are for the TDS520. Back when I was looking for an inexpensive used DSO, I stayed with the 2230/2232 and 2440 series for this reason despite their disadvantages. The known problems with many of the TDS series like leaking capacitors was a factor also.
Despite their low used cost, I tend not to recommend the 2230/2232 or 2440 series to beginners. They meet my minimum requirements for a DSO but their age makes for low reliability and beginners are not likely to be in a good position to maintain them.