usually produced using fossil fuels, using inefficient production methods that waste electricity

Well, it's either one or the another. While the energy loss is relatively high when using electricity, it's not a problem when you have an oversupply of renewable energy, actually it's even beneficial as it provides a storage for otherwise lost energy.
But regardless of the production, it generates no pollution when consumed by a vehicle. You know, like clean air in cities.

And of course, hydrogen won't solve tire pollution nor associated noise (albeit I guess it should be more silent that fossil fuel one) but it's still environmental friendly compared to what we have now.