I honestly can not think of any downsides, only a lot of advantages:
1. You got more control for high speed.
2. You got more control for jumping and landings.
3. You got more control and power for carving and riding waves.
4. You can ride toeside with more pressure and control.
5. You can jibe better, more room if you use straps, both behind the front ones or in front of the rear one.
6. You can always switch to narrow stance whenever you want - NOT possible to go wider if you dont have a wide strap setup.
Of course it is up to personal preference how wide is too wide, as at some point you probably dont like to stand that wide and like to stand narrow and relaxed, eventhough it might work better overall with wide stance - but you can still do that with wide straps
The only thing there is, could be that some find it looks cool to stand narrow in "Greg" style - but you can do that anyways, especially if straps are wider it is easier