It is an interesting speculation of what would've happened if there was a rail link across the Humber. Certainly, it would have massively changed the pattern of services in the area. I think you're right that there would have been a big incentive to run Doncaster-Hull via Scunthorpe since that's much bigger than Goole - so Scunthorpe would've probably gained at Goole's expense.
Another change is that that the London-Hull service could've ended up running via Lincoln (and there may have been more incentive to include that route as a franchised commitment 20-ish years ago rather than waiting until an open access operator picked it up - since it would have had more scope for serving large towns away from the ECML).
For what it's worth I believe BR wanted to close the line from Goole to Gilberdyke around the time the Selby diversion was built - if a rail link over the Humber existed with Doncaster-Hull services diverting via Scunthorpe then that would've almost certainly happened.
In regards to the Barton line, I've used it a few times for the sake of it. Was never particularly busy, even with just a 153 on it. I would agree that there probably isn't a tremendous amount of Hull-Grimsby demand - of the two main cross-Humber buses, the 250 (Cleethorpes) is definitely the poorer relation in comparison to the 350 (Scunthorpe), the former has half the frequency of the latter and the last bus leaves for Hull at 5pm. In this regard the train is better as the last one to Barton leaves 4 hours later (there is a bus for onward travel to Hull even though it's an hour wait at Barton for it).
The one time I tried to buy a through Hull-Grimsby ticket on a TOC site it refused to even output a journey, so it doesn't look like through ticketing is utilised too much. An all day ticket on Stagecoach East Midlands is £7.80 though (which would cover you for a return trip and any onward travel at either end you might want to do) so I don't think the railway is winning there.