No technically they do not. I started breeding them 20 years ago in 29 gallon aquarium tanks. They were very healthy and appeared content and had beautiful coloration.
BUT- today I prefer 175 gallon reptariums (29x29x48"high).
There are a couple of things to consider-
From the lizard's standpoint there is the quality of life. A larger environment allows for more room, a more simulating environment and arguably a higher quality of life.
From the owner's standpoint, a larger enclosure provides more room for an interesting setup in which to enjoy the lizard. I can be more creative with plants and lighting in the 175 gallon reptariums than I could in the 29 gallon aquariums. And it is a lot more interesting to watch a lizard that can stretch out and actually walk someplace. Really, even a 2' wide enclosure does not allow an adult male veiled a lot of room to do that.
As far as height itself goes- The idea is that a cage taller rather than longer is appropriate for an arboreal species. In a smaller enclosure like most of us are probably using (say 2x2x3 or even 4' high), my feeling is that height is not as important as height of the enclosure off the ground. A veiled is more likely to be comfortable in a 2' high cage located on a shelf 6' off the ground than in a 4' high cage placed on the ground.
Also worth consideration is your strategy for providing a temperature gradient. In tall cages this is provided by distance from top to bottom. A shallow enclosure would need this provided more from side to side.
Seems to me on the one hand you are asking for opinions, but on the other you are looking for a defining answer. My opinion is that it is more a matter of the former rather than a rule written in stone- but it should be balanced by your own opinion about quality of life of your animal...