One issue is the other inhabitants. If we're going to look at 'happiness' -
1. In the wild tangs are more of a schooling fish at least many of them most people do not keep them in schools - even in an 8 foot tank. My 2 yellow tangs - in a 5 foot tank - literally hang out together - basically have their territory - and do not seem stressed. The purple tang hangs out with the tusk - and they 'patrol' the tank together - but certainly aren't stressed.
2. I would assume - that breeding - makes a fish 'happy' - a single member of a species thus will likely not be as happy - whether in an 8 foot or 4 foot tank.
3. Tangs can travel (not for 'fun' - but for 'food') - at least thats the research I've found - but lets pretend its for 'fun' - to be 'happy' - the distances traveled in the wild are so different than an 8 foot tank - IMHO - they shouldn't be any more 'happy' in a 8 vs 6 foot tank.
I don't know - I'm not in a fish's brain

... I also am not supporting keeping tangs in small tanks etc. I do find it odd that there is a 'tang police' but not a 'trigger police' - given the fact that triggers travel further than tangs on average (at least certain genus'