Any individual player is only going to do what is right for them and their life, not "the reputation of the game up here". Why would Greg Stewart give a f**k about that? It didn't work out for him at Birmingham and so he had the choice of dropping down a level in England, moving overseas if an option was there, or moving to the second best club in Scotland where he can play in Europe and challenge for trophies. Aberdeen would have been very appealing in that case, especially given that he likely has family and friends up here which makes his life a lot better than it would be in Walsall or Rotherham or some other nowhere town in England.
It's a bit like the discussion that more Scottish players should be playing outside the UK. Of course it would be good for Scottish football to have more guys picking up a different style of football, but that doesn't mean it's the right decision for for any individual player to do so. You're basically asking a young guy to move away from home and adapt to a different culture without a support network around him, and while there are lots of potential benefits to an individual, there's also that chance that it can all go wrong. When you can live in England or stay in Scotland with the Old Firm and earn just as much or more money then there's not a great deal of incentive to take that bigger leap.