Re. the Walkabout D.I., yes, the master volume affects it, but having a D.I. level allows you to get things at least ballpark the same (as far as the signal you're sending to F.O.H.) at very different stage volumes.
When I had mine, I either left the D.I. knob at noon or turned it until I got the thumbs up from the tech. Levels varied, but I don't recall ever being told that it was too hot.
As far as whether having a constant level sent to the mixing board is more or less desirable than having the level vary with stage volume, I go back and forth. I know that conventional wisdom favors the former -- and I absolutely see why -- but most guitar cabs are mic-ed. When the guitarist turns up, the level of the guitar to the board goes up, too. Assuming that you started with a good balance and that the guitarist turned up a reasonable amount for a reasonable reason (sound changed as the club filled up, lineup changed at a jam, or whatever), having your volume change (assuming that you're being reasonable, too) might make sense. I've often played in situations where there isn't someone on the board consistently...
I get that, if you're on the board and people are going crazy with volume, it can be a pain. I like to feel the bass and feel the kick, but the levels some people play at are insane -- not only dangerous, but bad-sounding due to overloading the room. I've been the guy to tell everyone to turn down and listen to each other more than once, but I've kind of given up on it lately unless something is egregiously out of balance -- but I digress.
I don't usually fiddle with the knobs after the first few minutes, though, and then I tend to stay pretty close to the initial level I set, so having the FOH signal vary with master volume hasn't been a big deal -- even with amps that don't work that way, it will vary with gain.
Everything else being equal, I'd take a D.I. the level of which does not vary with master volume over one that does, but the sound is the thing. As long as the range of levels is reasonable, I'll take the variability in level over a compromised tone.
I seem to recall the Walkabout manual mentioning that Mesa would mod the D.I. so that it wasn't affected by the master volume, if you wished, but that, in their estimation, you would lose something in the bargain. I never played a Walkabout so modded -- I did play mine through a poweramp once -- can't remember if I fed the amp via the effects loop or the D.I. It sounded good, but wasn't quite the same. The feel was certainly different. Don't know if that would (if via the effects loop) shed any light on what the modded D.I. might sound like or not.