"Do people actually visit Edinburgh because it is a WHS city??"
Yes, but far more visit because of the things that have made it qualify to be a WHS.
There will always be a tension between preservation/conservation and development/improvement. It's unfortunate that the latter is usually led by developers/architects who want to make a mark (and money).
Edinburgh is fortunate not to have been bombed and too slow to build its proposed inner ring roads when they were fashionable throughout the UK.
In mainland Europe after WW2 road networks were built but many cities - even ones that were extensively destroyed - rebuilt in keeping with what had been there previously.
WH status hasn't really made Edinburgh say "no" enough, and now ScotGov has policies broadly in favour of development/ers (without adequately explaining its notion of 'sustainable development').
It can of course be argued that anything is better than a gap site (Edinburgh, notoriously, used to have quite a few) and better than a rundown bus garage/arts venue.
In the past development was fairly random and people now like the way (in many places) contrasting styles and ages jostle together.
But Edinburgh is the city of the formal New Town (I'm sure some people would have preferred the green fields to have remained at the time it was built) and the relatively coherent Old Town.
Edinburgh has avoided the towers and status buildings of London - which most people would regard as a good thing.
Few will miss what is currently on and behind Leith Street, but if the orange peel hotel is built the joke will be on the city.
The proposed hotel opposite St. Andrew House is fairly gross - irrespective of the setting, though the possibility of it reflects badly on the City (particularly, but not only, the Council) and its failure to make good use of what is there.
Edinburgh doesn't really deserve WH status unless it's just for a collection of legacy buildings.