There is not a single airport that will cater perfectly for everyone. People have to travel to an airport and it will always involve a degree of hassle. Heathrow has connections to it and for some that's easy for others it isn't. Same for Manchester.
If Leeds went to 8 a day to Heathrow then good for them. Why not if it makes money but it doesn't mean that Manchester should then sit back and not offer flights around the world as well. For many in Yorkshire it's not really that hard to get to Manchester and it gives them an alternative to London.
The amount of tax payers money is unknown but it will be in the billions and when you have the majority of the country desperate for investment then it's not difficult to see why people are pissed about Heathrow getting money because we are told that there are no alternatives when in fact there are.