In the case of leaded gas we got literally no benefit. There was never a legitimate reason to put lead in motor fuels.
That's not true. The benefit was anti-knocking without using more expensive high-octane fuel (or later, ethanol).
It was still a terrible, terrible decision though, given the centuries of knowledge that lead is a poison.
When thinking about the explanations, keep in mind that leaded gas adoption was near-universal, including economies where "companies" or "competing fuel" weren't really a thing in that sense - e.g. USSR. They still went for leaded gas because of its objective benefits.
And even today, we still use leaded gas for aviation...
It is a horrible trade-off either way, but it was not done for no gain at all.
That's the easy model where you basically know what you are doing is wrong but you like it so you decide to do less of it. The net result is still positive.
An alternative approach is to try to actually innovate and/or invest in means of transport that don't require tyres nor friction for braking (e.g. eddy current brakes).
That was the stated rationale, anyway. It was an anti-knock compound. So, was that false? Did it not help knocking at all? Or was reducing knocking not a benefit at all?