> The only downside I can think of is that it would send the message that Monero cannot stand on its own since it offers a bridge to Bitcoin.
In my opinion this isn't a big deal. It's pretty clear that for the near-future there will not be "the one" crypto currency, but all of them will interop with each-other. I think this would be a great feature.
My only concern with it is that it would seem a lot like favouring a single for-profit business when it comes to converting to BTC (xmr.to vs ShapeShift). If MyMonero is not branded as "the official Monero web wallet", but "Monero endorsed web wallet" it would be OK. Otherwise it should be possible for people choose their BTC converter company via some sort of plug-in architecture (ie what onemorexmr said).
If MyMonero or some wallet was to integrate xmr.to/shapeshift, they would have a very strong value proposition for people using Bitcoins who value their privacy and want something that is easy to use and just works.