Would you prefer a voltmeter or a scope when measuring average voltage precisely?
Scopes are designed to plot waveforms so you can see what the wave-shape looks like. While modern scopes have the ability to do a lot of other things with the data gathered from the ADCs they are not designed as precision measurement devices. 

The downside of a basic multimeter is you typically don't have control over the averaging length. If the averaging length is too short compared to the waveform you are measuring then your result won't be an accurate represention of the long term average (and your display will jump around). If it's too long then the reading on your meter will take an annoyingly long time to settle. The more accuracy you need the longer the averaging period you need.

Looking at Why do DMMs have so low update/refresh rates? it seems that ordinary multimeters make about 4 readings per second. High end bench meters often have settings available to adjust the averaging behaviour.