Thank you for that insight!

I can't see any downside to not checking in online. You are more likely to get upgraded, less likely to be downgraded, more likely to find out if your ticketing is still correct, gives to an extra 10-15 minutes contingency if you get the legendary flat tyre/tire, get AppUp upgrade offers, find out if your API has been rejected by the US or Canadian authorities (not reliably), see the risk of SSSS (not reliably), more likely to be contacted or auto rebooked if there are problems (somewhat reliably). You don't have to get a boarding pass print, that can be done at the airport, at a later time (e.g. via email), or via a hotel (using the fax option) or indeed using the App - tens of thousands of BA's passengers use the App every day without problems. In a way, though, not printing the boarding pass is a good idea anyway - once checked in you can then grab any better seats, for example if someone else accepts an upgrade offer and vacates some plum seats. A printed boarding pass will preclude that.

So yes, do get checked in as soon as you can.