Typically, seating is outfitted by the airline not the plane.

This is technically true, but in practice planes are designed for or or two seating configurations. For example you're always going to have wider seats in an A320 than a 737 because no airline is going to configure their 737s 5-across.

To the best of my knowledge, no airline has configured 787 economy anything other that 9 across. There's not actually a direct comparison to Airbus, the A330 is slightly narrower but is usually configured 8 across, whereas the A350 is slightly wider and is also usually configured 9 across.

So as a general rule, and subject to exceptions such as the proposed 11-across A380, Airbuses will have wider seats in economy than Boeings.

But the seat width is determined by the seating configuration and the plane is designed so that one or two particular seating configurations will work well. (Although it matters less for widebodies where there's enough wiggle room to say "this plane will fit 8 reasonable economy seats or 9 ridiculously narrow ones".)

Nope, airlines decide on the width too. The entire internal layout is up to the airline including the lavatory design.

747 has both 9 and 10 seat wide configuration.

That's why I made an exception for widebodies, although I accept that "making an exception for widebodies" more or less undermines my point.

But I claim that, for example, you can't realistically have a 737 layout that isn't 6 seats wide in coach — and that means the width of your coach seats will be whatever width fits 6 seats plus one gangway.

You can and they did.

Air India and KLM operated 737s with 5 seat config in economy (flew in them) up till last decade.