"But psychologists seem to agree that it's a good gap. I'm sure I read a study claiming a 1 year or 3 year gap works well for the child, and a 2 year gap is the trickiest."
Yes I've read that too.
I have a 3 year age gap (almost exactly) and it was perfect for us.
Benefits were:
DC1 had a chance to be the baby before it became the big sibling.
DC1 old enough to help with DC2 (fetch nappies, wipes etc)
DC1 was out of the pushchair, so between pushchair / buggyboard and sling, I only ever needed one pushchair, even for long distances.
DC1 old enough to understand and wait if DC2 needed help.
DC1 out of nappies.
DC1 at paid for childcare when I had DC2, so I got a bit of time to spend just with the baby.
Only paying one set of childcare fees at a time (worked part time).
Now they're older, I've found it's continued to work. Close enough in age to share similar interests, to play together and to be good friends, which they are. I feel bad sometimes because DC2 never calls for friends, even though people are always asking if DC2 can go out to play. DC2's default is to play with DC1 wherever possible.
But at the same time, there's enough of an age difference that they're not competing against each other. The age gap is big enough for them both to realise that it's not fair to expect DC2 to be able to do what DC1 can do, which is just as well as DC1 is very competitive!