What will be the backup for when there is no wind or sun for several days or weeks? Electric customers get upset when their lights blink for a few cycles.
There is a real issue with long term storage, but in the meantime overbuilding can achieve climate goals at reasonable cost and far less time than it takes to build a new nuclear plant. (Hinkley Point C was approved in 2012 and is still not online!)
Germany's decision to shut nuclear in response to Fukushima looks terrible in the rear view mirror. But I suspect it was informed by how bad the costs of Chernobyl were in terms of discarded agricultural production.
In any case, I would agree it looks like a mistake in hindsight.
There can be tons of explanations for that: going out of nuclear was more popular than building renewables in people's backyard, going out of nuclear was an easier path to follow than develop the renewable sector, the effort of going out of nuclear may have been used as an excuse to say "see, we do green stuffs, no need to do more", the coal/gas generation may have looked an easier or more profitable path for some politicians, the industry had less resistance against going out of nuclear than going out of coal/gas, going out of the nuclear may have been an easy concession to give to the Green and to look good to the public, or even the government had low incentive to succeed in the transition because if it fails they can blame the Green parties ("but it was your plan ... see, Green parties don't have realistic ideas")...