Agreed on all points except that solar can never replace petroleum. It's absolutely impossible, even if you covered every inch of the planet with solar panels, there is simply not enough energy to run much of anything.
Yep, you'd need to have a solar array perhaps impractically large -- maybe the size of Nevada or something for the US -- but it isn't the size of the whole country.
Here's my group mate from grad school giving a TED talk on just this topic, explaining how for the UK (which has no deserts), it would be a solar array about 25% the size of the country:
https://youtu.be/E0W1ZZYIV8o?t=549Space-based solar power might be able to add appreciably.
In the far future, there is the Dyson sphere.
But, I think nuclear is a good way to go -- if people could quit making very stupid design, operation, and policy decisions about it. Safety concerns and disposal of fuel are straightforward to deal with. We just have a legacy in the world of crap designs and bad decisions that set things down a bad path that is hard to reverse.