It's not the recycling, it's the sending them back through the same supply chain that would be the problem.
Reuse of glass bottles is not recycling (it's reuse.) And there is no problem, it works great.
Use of glass bottles is somewhat controversial in that glass containers mean considerably heavier weight in transport, which in turn means that more energy must be burned to move those trucks. The introduction of plastic packaging immediately led to fuel savings in transport.
That may be the case, but sanitation certainly should not be a concern with glass reuse. Glass is easy to sterilize.
Reuse of plastic soft-drink bottles in northern Europe is somewhat controversial, inasmuch as vast amounts of water must be used to wash and sterilize them.