I don't think name dropping the Dominion War is necessary, but for the AQ, it was comparable to WW2 as far wars go. . I think Picard is making the same mistakes the TNG era show did by refusing or avoiding mentioning the Dominion War because it would be too confusing to some viewers.
It's too much of an over reaction. Either some fans will be become curious and watch DS9 to know more, or simply don't, or if they already know about it, it's no issue.
I could never understand avoiding mentioning another series to avoid confusion, as if that would do serous damage to a show or franchise.
The same thing could be said about Seven of Nine, Icheb, or the Romulan supernova or even Hugh.
DS9 takes a backseat again! lol.