Quite frankly, it would be unenforcable for the Armed Forces...
Unless of course, all pay scales were reduced to a single 'basic rank related rate' and a Local Allowance was paid depending where the posting was!
Extending on Sunderland Matts comment;
One of the few benefits of teaching in Sunderland (to use the example given) is that your pay packet would go a little further that in Surrey. If teachers (insert any profession) were to get paid more to live in Surrey then who in their right mind would stay in Sunderland?
What I also don't get, is that although the cost of living may well be less in Sunderland than Surrey, that's not all; a teachers working conditions will be a lot better in Surrey than in Sunderland and then we have the situation as Matt says, "Who in their right mind would stay in Sunderland?"