Well, that's the point, but it is not a straightforward question. Do the benefits to society as a whole (I.e. The taxpayer) outweigh the costs.
In the case of TFL the point is that it is needed to cope with the extra traffic. The present solution is okay, and clearly there are desireables to improve what's there but those turn into necessaries with expansion.
Clearly for heathrow the answer is yes it is worth it because they are getting £[x]bn of benefit at the expense of the taxpayer. From the taxpayers perspective there is a genuine question.
I agree about LGW, if it is going to be anything in the South east, it should be Heathrow.