Or use congestion pricing and other taxes on cars to make it so that those who would take a car see economic gain in taking the free transit instead. Use these levees to fund the transit services. The main problem you've identified is underfunding Transit. So, uh... don't do that
Even "non free" public transit usually still needs public subsidies to be affordable (similar to how road use usually isn't charged directly), it's just that imho the "free" part is less important than usability.
Sure, I think that's absolutely true No point in having a free service that is not usable or accessible. But once that is established, the idea of having free fare transit is pretty good.
I think "affordable" is good enough (that includes subsidised tickets for lower incomes) but I'm also not opposed to "free" on top.
Ultimately I agree, I'll take what I can get. I think the ultimate goal should be free public amenities.