The problem is that no other IAG brand has the London presence or clout of British Airways. Aer Lingus tried Europe from Gatwick and stopped. Vueling isn't that popular or well known in the UK.
Personally I would rather fly easyjet than Vueling.
In my non expert opinion this move is a mistake both in the short and long term. LHR is looking to put up charges to airlines considerably to recoup losses. The European leisure market is predicted to recover faster than long haul. That
leisure market is what Gatwick does well. Trying to get back in to Gatwick in a couple of years may well be difficult too.
British Airways will not be able to offer such competitive fares/holidays for its holidays from Heathrow, as it is a much higher cost airport. I don't believe for one minute that all of BA's Gatwick customers will follow it down the road to LHR.
We shall have to see what the plans are for BA long haul at Gatwick. I have been hearing anything from 11 to 15 airframes. If Heathrow does raise charges for long haul travel, there may well be move moves of routes that have a higher amount of point to point traffic.