Whilst the ProjectMapping map has only ever been intended to show routes used by regular passenger services, the
Adlestrop map gives a good overview of all current and past lines:
There is indeed a chord linking the Doncaster-York direct route to the Hull-Leeds line. At one stage there were proposals for one of the London-Leeds services to run this way into Leeds, particularly for those which continue on to Harrogate/Bradford/Skipton and vice versa, to save a reversal at Leeds.
However, this didn't materialise, and the chord is now usually only used by diverted passenger services when the route via Adwick is shut, and by a handful of freight services. Whilst the section of the Hull-Leeds line between Hull and Micklefield isn't particularly busy, the section between Micklefield and Leeds is virtually full to capacity with the combination of non-stop services, stoppers and a few freights. So something would have to give to allow London-Leeds services to regularly run this way.
Whilst it's a nice thought experiment to imagine where you might run open access services, if you want it to be vaguely realistic you have to consider the constraints which the ORR would impose. In the current climate, their position seems to be that anything which abstracts more than a nominal amount of revenue from Treasury/DfT coffers will be rejected. See, for example, their
rejection of the proposal for open access services between London and Cardiff last year - despite the fact that the application broadly met the same criteria as successful pre-Covid applications.
The ECML also has a highly competitive open access market, with Hull Trains and Grand Central serving Doncaster and several of the smaller intermediate stations. That's aside from the question of whether there would be any paths available south of Doncaster...
