The Corby to London train currently stops at Luton hourly, maybe this could be moved to Parkway, but then means the towns main station no longer has an express service and I am sure the council will be unhappy with that.
I don't think the council would object if it added capacity at their airport. There are 6 trains an hour that shuttle between the airport and the town so it is not as though the town would lose its connection up north.
With regard to extra EM trains stopping at Parkway what we are talking about is an extra 2 trains an hour if the Luton service was moved to Parkway. If all trains stopped it would then not block the fast lines but more importantly it would spread out extra demand to London and give Parkway direct trains to more towns and cities up north that are not directly connected to Parkway.
Also not all passengers want to interchange at St Pancras. Two Thameslink trains an hour stop at every station to Wimbledon picking up those who do not live near a major station while four trains an hour also cross London as they head for Gatwick and Brighton.
Next year sees London Bridge reopen again to Parkway passengers but more importantly Farringdon has been rebuilt as a major interchange station for the Crossrail line linking east and west London which will remove many of the passengers from St Pancras.
While clearly demand will increase, with at least 10 trains an hour stopping in each direction and 12 car Thameslink trains being introduced weekly I have not heard of new franchise requirements restricting capacity due to potential overcrowding.