Ex-EU: what happens if BA cancel the outbound flight?
Same situation for me a few years ago (have wisened up since). Outbound to AMS delayed to mean I would miss AMS LCY and then LCY JFK.
First check in agent very much told me that it was my problem as they would get me to AMS - just late. Eventually and offered WT and WTP to JFK on a later flight but combination of persistance, charm, insistence on a supervisor eventually got me booked in CW on ex LHR flight.
That doesn't need to be the case though - BA could play hardball.
Downside of ex EU and mitigated by same-plane turn-around, night in ex EU airport or previous day position and first leg rotation.