One big issue with this is that once you are in Approach mode, Boeing makes it pretty hard to get out again. Push TOGA, retune the ILS or disconnect and recycle the FDs. The only one you're conditioned to is pushing TOGA.
I learned this the hard way in MAD where they told us to level off after we'd captured the glide and been cleared for the approach. It's not difficult, but once again it requires training, awareness and thinking about it beforehand.