That's not what I remember, Ultima III had crude 3D dungeons similar to Wizardry's dungeons. The maps of the dungeon levels were 2D and tiled. Google image search for "ultima iii dungeon" confirms my memory.
In fact, all of the Ultimas through V had first-person dungeon views.
Wizardry's wireframe dungeon renderer was a bit more advanced, though, in the sense that it supported empty space and disjoint 'islands' in the map, while Ultima I and II could only display corridors.
IIRC that limitation was fixed by III, but it may have been IV. It was definitely fixed by V.
I dunno about Ultima III, but QotA had 'battle screen' sections of dungeon, which basically means a top-down section. I believe the altars are in such sections? I do know there's a three-way split in the Stygian Abyss, because I accidentally went around in a circle last time I played.
QotA is really awesome, I should play it again some time.
It had both top-down 'combat rooms' and a 3D first-person view (as did Ultima III.)
Of course, in Ultima III, you couldn't leave the top-down combat arena until the monsters were dead or you were. That was also fixed in Ultima IV, where you could chicken out at the cost of some Valor.
Dragon Quest did not have Wizardry-like dungeon crawling. It had Ultima-like dungeon crawling. Ultima III had top-down tiled dungeons in '83.