Transmission losses aren't really a big problem for the grid. Cost, geopolitics, and resiliency matters more. I don't expect superconductors to change much here.
The whole "plate a desert with solar power and solve the world energy problems" doesn't work because the desert isn't where the power draw is. Superconductors hypothetically permit the African desert to supply Europe with power.
As this goes from science to engineering, we may find other issues with that plan, beyond the obvious expenses (for example, current limits can be handled with more wires, but if the current limit is sufficiently small that's still a problem, this is no solution if the superconducting bundle has a hundred square meter crosssection), but superconductors at least put it on the table. Conventional conductors do not.
Superconductors could make transmission lines much more compact, sturdy, weatherproof, and less vulnerable to sabotage. You could run a thick armored cable instead of a set of open-air wires on tall towers.
We will still need some step-downs, because current density is limited. But we will need fewer of them, and they won't need the monumental cooling they have now.
I agree that the nature of this is entirely different to transmission losses, but I don't expect 230V lines carrying tens of thousands of amps. This would probably require excessive amount of SC material.
Storage would help, the cheapest production cannot run continuously.
Generating costs are a small fraction of the final price of electricity, taxes and transportation are the big ones.
If you just look at superconductors as a replacement for any old piece of wire you're going to miss out on a whole bunch of advantages, it is a clear qualitative difference which enables solutions that are entirely undoable today. Yes, there is HVDC, but the lines are expensive and due to the high voltages involved are not easy to interface to or from. They do have some unique advantages, being DC they allow non-synchronized grids to be connected.