London Underground drivers do not have a mainline driving licence simply because they are not qualified mainline drivers. Those who work over Network Rail infrastructure have an add-on to their LU licence specific to the section of line they work ONLY. The rules for this are glossed over in half a day or so (compared to 3 months rules for a mainline driver) and in no way reflect anything close to all the information contained in the Network Rail rulebook. LU drivers are also not issued with the full NR rulebook, the sectional appendix or WONs and PONs.
LU trains are fitted with completely different safety equipment to NR trains and do not have AWS or TPWS fitted. On the whole, LU drivers have far more SPADs on the NR sections than NR drivers do, which is probably to do with the aggressive style of driving used on the LU sections, the fact that LU signalling on the Bakerloo and District is two aspect with signals far closer together, line speeds slower and most reds sighted within service braking distance. Its also partly to do with LU trains not having AWS or TPWS fitted. The multiSPAD lists for the areas concerned make interesting reading.
There is nothing stopping LU drivers from applying to join the mainline as trainee drivers if that's what they want to do. In fact any LU driver serious about going on the mainline would do just that.