Current stats put it at 18.6%: https://www.eia.gov/tools/faqs/faq.php?id=427&t=3

It's a little less than renewables and a little more than coal.

> I would be nice to see it be a nighttime base-load provider

The bigger issue with Solar is the dramatic difference in generation between the summer and winter. So not only do you need something for "nighttime," you also need something for "winter."