I agree. Others have speculated that the last remaining seats are released only at the 3 hour window - thus, there is no benefit to waiting to check in.
I'd be curious to see if that's actually the case.
Personally, I would check ITN before checking in. If there are no F seats, it's a no brainer - check in as early as possible - to secure an exit row seat...
If there are seats that haven't been released yet - especially if the silver window has come and gone, it may actually pay to wait.