This logic fails on a couple levels. One, bike lanes are often not wide enough to support another car anyway. Two, Braess's paradox[1] is an effect that's been noticed for as long as we've had cars that adding a lane to a roadway will often show no improvement, and perhaps even add detriment, to a local traffic system.

So I guess it's a common sense solution if you don't understand the first thing about roadway design?

[1] https://en.wikipedia.org/wiki/Braess%27s_paradox

They understand it, they're just in the middle of a culture war.