amplifier with volume control

I have a Quicksilver Integrated Amplifier. It is a tube amp, it has a volume control, and it sounds great. It is rated at 20 watts. A simple no-controls JDS Labs+ DAC feeds the amp, and the amp feeds Focal Aria 906 speakers, specified 89.5 dB sensitivity. I listen at moderate volume; the control stays around 10:30 o'clock. Well, it is around 12:20 o'clock when the input is from a phono preamp.

I have an old Acurus DIA100, which was marketed as a Direct Input Amplifier. It is the first version. Whether or not it technically is a direct input amp without a pre-amp I do not know. I use it to drive my outdoor speakers and it still sounds great. Back in the day it was the center of my main system and a very flexible input/output device. Maybe you could check one of these out. Hope this helps. 

The presumption that an amp with volume control built in will automatically yield superior sound quality is wrong. It may. It may not. Only comparison to other genres/systems would tell. 

NO one can tell you which configuration would be superior in any combination of gear; pre/no pre, passive/active pre; dedicated DAC direct/integrated DAC direct; dedicated DAC with integrated amp, etc. 

I have tried all these and the winner? It depends on the setup and gear. 
Anyone who tells you differently is simply stating opinion. You simply have to try combinations if your goal is to actually find the best method with the gear on hand. Short of that, just presume and pick; it's what most do. 

I have built a lot of systems using DAC direct, either dedicated DAC to amp with software attenuation, dedicated DAC to integrated amp, or integrated DAC with hardware (built in) attenuation. Again, results vary based on the equipment, cables, etc. used. One can have a favored setup, switch speakers and find that a different setup is preferred. 

It is nowhere near as simple as recommending one setup as superior. The more systems built, the less a simplistic setup recommendation suffices. Unless you build a bunch of rigs, you simply will not know which is best method with your gear, and neither will anyone else. 

FM Acoustics amps have gain control for each channel in the back panel and Vitus Audio used to have the capability for variable output or fixed for 2 sources (not familiar with current models). For example, the VA  SS 101 sounds great alone and there is no need for preamp.

I prefer the name of potentiometer for the volume switch.  It just makes it sound like it is holding all the answers.  This may sound strange but I have my "cheap system".  This runs a class D amp to some transmission line speakers that I built.  I only run through this through bluetooth.  So, should be a crap sound, not going to argue things could be much better.  To maximize this, I run the volume switch on the "integrated D amp" at 2/3 potential.  I then adjust the volume from digital source.  This makes the speakers much more alive and dynamic at all volumes.