As far as I know, most HRVs are cross-current. I don’t know why.

Avoiding condensation?

Rotating disk heat recovery devices can also recover humidity.

I think most HRVs have condensation drains, so I doubt that avoiding condensation is the major consideration.

I would guess it’s more of a geometric consideration. A square cross-current heat exchanger can have each port on a different side, so the whole perimeter is used. A counter-current exchanger would have two ports on each of two sides and no ports in the other sides, leading to a rather more complicated and larger arrangement.