The problem with staying the last night at an airport hotel (and this applies to lots of cities, not just London), is that you are pretty far away from the city you came to visit.

I'd rather be in the heart of the city, convenient to good eating places/entertainment/theatre etc. rather than stuck in a boring airport area.

I can't even remember any time that I've spent my last night in an airport hotel, anywhere in the ~40 countries I've visited in my lifetime.

After all, you typically check into a hotel in the early afternoon. If it's an airport hotel, where do you go and what do you do for the rest of the day?