Right now, in my area, we have a Nuclear plant that handles the base load, but we tend to keep it at "not full capacity" most of the time, because nuclear is harder to ramp up/down in response to load.

In the video, he shows how renewables can pick up the slack in many ways... but I was thinking, why not run our nuclear plants at something like 90% capacity all the time and store the excess energy in utility scale batteries?

It seems like these devices could have a far greater impact than renewables could, and they can harness existing investments in nuclear. It's too bad we can't just pump water uphill into reservoirs from nuclear plants and dump that through turbines when needed. Such a setup is obviously a huge investment and you can't really build a reservoir next to every nuclear facility.