Thameslink generally works with 2 platforms because there are two completely separate platforms at each station, not 1 island platform, trains are identical, flows are largely one direction in each peak, there is very little interchanging, passengers tend to be pretty familiar with what is going on and there are very long platforms and trains to soak up the crowds.
There is loads of interchange on Thameslink, including plenty of passengers with luggage and irregular users - it does after all connect several major termini, plus Gatwick and Luton airports.
What's true of any high density metro style operation is that it's the pedestrian flows at and around the platform that are the key bottleneck. Note how much is invested in London in deeper platforms and enhanced pedestrian interchange e.g. recent improvements at Bank, KXSP, Faringdon, etc. None of these schemes
effectively involved provision of
additional tracks or platforms (albeit some were replacements) it's all about improving pedestrian space and circulation. Multiple platforms just introduce additional pointwork, which increases headways and reduces throughput.
IMO there is no practical reason why a selection of similar schemes in Manchester could not achieve similar results. The only real difference is the freight flows and many of these these could be rerouted away from the city centre with some moderate interventions elsewhere.