Delivery drivers should find parking. They should be fined heavily for parking in traffic, including bike lanes.
Larger scale deliveries (e.g. to malls, grocery store, factories) should have a privately owned off-road, built into the structure place for trucks to park and drop things off. Though things like factories often simply don't belong in the dense part of the city.
This would all be solved if we just had delivery parking spaces and got rid of on street parking for everyone else. Really, just that part is just where everything falls apart quickly. This is why traffic seems so much better in Europe (at least where I've lived, like in Switzerland), deliveries work, cars are not parked on the street except at a few very expensive parking spaces.
The complaint I keep seeing is one of public subsidy. So you're suggesting we subsidize deliveries but not general parking? (To be clear I think it's all just anti-car absurdity.)
Of course merely repurposing a few spots to "commercial deliveries only" every few blocks would probably work. I've seen that done in a few places. I think it comes down to a planning and administration failure.
But ya, if you want to roll back car use, you can do that fastest by restricting free parking. Your community better be prepared for that with adequate public transit investments. Better to just roll back free parking slowly while ramping up public transit investments, but America always messes it up one way or the other.