My instinct tells me that focusing only on a cheap flight often gives a false budget impression to travelers.
It's a bit like judging a movie by its trailer; it gives an idea, but says nothing about the quality of the full script.
A budget flight to London doesn't make accommodation or food costs cheaper once on site, it's even the opposite.
Savings on the ticket can be quickly swallowed by unexpected daily expenses, like the price of a coffee or transportation.
What I call the "trailer effect" in travel budgeting will only be truly falsified if search tools directly incorporate local costs, like those from Numbeo.