As a kid I grew up in reactors. My brother was a physicist. I've seen interior photos of tanks holding nuclear waste years ago. They're still there. Yes, it is a problem. Those that think it's not a big deal don't know how a reactor works.
We do have an answer, we have several in fact. The problem is capital, regulations, and NYMBY. Breeder reactors can run on nuclear waste, but they're incredibly expensive to build and could be easily modified to create weapons grade nuclear materials. So maybe not the best idea while we're all still thinking about blowing each other up. We can bury it deep underground, look at Onkalo, Finland.
https://en.wikipedia.org/wiki/Onkalo_spent_nuclear_fuel_repository
Many other locations have been suggested in many other countries, but the moment something is labeled high-nuclear-waste storage it's impossible to get approved. In my opinion storing it deep underground is fine, it's transporting it to that facility that worries me.
Point in your favor though, why put more money and effort into nuclear than is necessary when that same money can go to renewables? Nuclear power absolutely makes sense in select places and shouldn't be ignored. It should grow a little but it's already obsolete compared to alternatives.
Yes, well...we'll get right on that. I'm sure someone will want to spend the trillions of dollars into expensive breeders that cost nearly twice as much to maintain and operate at scale.
Your last paragraph applies. While we don't approach these difficulties we lose the opportunity to build.