Base load, for starters, is an overblown problem, multiple days with close to 100% renewables showed us that. Now that this is out of the way:
Massive build out of renewables, mainly solar and wind. Build the grid for that as well. Use gas peaker plants, if needed. Keep nuclear plants running as long as safely possible. Invest in a green hydrogen network for storage. Make industrial demand more flexible. Reinterate, rinse and repeat.
I work from memory here, based on what I learned during my masters and a couple of stints in energy hungry industries a couple of yeaes ago. Besides gas peaker plants and green hydrogen, all of that is already happening in Europe.
Especially solar and wind build out is progressing massively across the world, even without a concentrated effort behind it.
Regarding industrial demand flexibility, that is also happening for a decade now (I personally know it does in the chemical industry, paper industry and graphite industry, surprising how much flexibility companies can squeeze out of production tech that was historically seen as being not flexible at all when there is loads of money to be made). Domestic demand is different, convenience beats saving most of the time, also households don't have professional energy management (hint: there isba massive, hard, start-up idea here: provide automated consumption control of electricity for households beyond smart thermostats ansball the other "smart" home crap).
Nuclear is a dead end in the developed world: too expensive (Hinkley C was already more expensive than wind like 7 years ago), takes too long install (just google year per kWh for the last NPPs installed) and has additional, unsolved, long term issues (waste storage only being one of those). Heck, even investors are quiting NPPs across the Western world. Nuclear has a future so: existing plants need be run as long as safely possible (the main reason German plants were shit down, they reached the end of their service live), for countries with nuclear arsenals, for the production of medical radionucleoids, for research... New ones are a waste of time, energy and money right now so.
And yet again, you said why something doesn't work, because just building dozens of plants and go fully nuclear is not feasible or realistic for the developed world.
For developing countries it is different, and they should build nuclear plants instead of coal ones, but then those have a lot of catching up to do. They could also go fully renewable right away so, they should have an "easier" (nothing is easy about any of this) life doing so without a century of legacy structures and systems to worry about (grids, industry, domestic use...).