With most sections of the railway operating at bus frequencies, if we still can't get connections to work, then the solution isn't to run even more services, it's to tidy up existing services to make them connect. There isn't the network capacity to run more services.
Thameslink does need recasting. The Peterborough/Cambridge - Horsham - Brighton services are symmetrical. The Bedfords are not. Making Thameslink symmetrical should be the first step.
A symmetrical Thameslink would help defining the symmetry of EMR Inter-cities. Beyond sorting out the symmetry, currently the Sheffields are one fast one slow, half hourly at the London end but closer to 10/20 at the Sheffield end. I'm not sure that's helpful given the number of services on approximately half-hourly patterns the other side of Sheffield. Having non-standard patterns not only mess up passenger connections, but make platforming more difficult - you don't have repeating half-hourly platform patterns.
I think it would be better if 1tph stopped at EMP and the other Loughborough and Long Eaton. This keeps speed differential to an absolute minimum, and with slightly different dwells at Derby and Chesterfield the two paths could arrive and leave Sheffield exactly 30 minutes apart.
Then recast Cross Country for common symmetry. The current Derby - Sheffield pattern (the combined pattern with EMR) is definitely not symmetrical. Have the two paths exactly half-hourly apart at Birmingham. The current pattern of 25/35 at Birmingham then 15/45 at Sheffield in the northbound direction is just silly. Have 1tph call at Tamworth and the other at Burton so they two tph have the same journey time between Birmingham and Sheffield and slot between the EMRs at as even intervals as possible. This skip-stopping is okay as long as the Cardiff/Birmingham - Nottinghams stop at both Tamworth and Burton.
With the combined EMR and XC symmetrical and tidy between Birmingham and Sheffield, there'd be a lot more timetabling clarity in terms of where the 1Ns should go on the graph. You then wouldn't get into the ridiculous situation where despite having 2tph one side and 4tph the other, a Leeds - Birmingham or Leeds - Leicester journey only has one valid opportunity to travel per hour.