We're going to need a lot of solar panels and an efficient way to transport power from a very sunny place to another location where the loads are. For instance: https://en.wikipedia.org/wiki/Pacific_DC_Intertie The pacific DC intertie right now often ends up being used to transport power from hydroelectric dams in WA/OR to California. But there's nothing to say that something couldn't function the other way if there…
It really doesn't. I'm a huge fan of back-of-the-envelope maths, and this idea raises some very fun questions. How big would the power line be, if the UK (where I live) was powered entirely by solar panels in the African desert?
The UK's average instantaneous power consumption is around 100GW. Assuming a capacity factor of 5 (which is probably far too low), the power transmission system needs to handle at least 500GW. The current (and somewhat unproven) state of the art in power transmission operates at 1000kv, and can carry 5GW per pylon system. We would need 100 of those operating in parallel. As each of those has a minimum separation corridor of 100 meters, we would need to persuade all of the countries along the route to give us a 4000km x 10km strip of land, as well as the approx. 150sq km of land needed for the panels themselves.
This leads to another fun question - if you want to install 150sq. km of solar panels in the desert and still have enough useful life left in the panels when you're done, how wide does the road need to be to carry all of those, and how many trucks will you need working that several thousand km route?