"Which is OK in today's climate."
Yes ...
"A couple of thousand years from now, if the roof leaks, so to speak, and the area gets significant rainfall, those hot containers might corrode away. I wouldn't want to be drinking from a well near that..."
and
"Some of those isotopes are nasty stuff, though."
This is true, but people make 2+2 = 5 when they put together "radiation that lasts for thousands of years" with
"some of this is highly radioactive".
Reality check: The longer the half-life, the lower the level of radiation. Then you have to consider the decay path; is it something nasty (high energy particle that can penetrate human body) or low energy. The radiation level in these casks is not constant; it goes down drastically year by year for a few hundred years to a level of very low radioactivity, radiation level that is many orders of magnitude smaller than the level of when it left a nuclear power plant.
All of the "hot" radoactive decay elements in nuclear waste have half-lives measured in days, years, or tens of years. After about 100 years, the radiation level is much much lower. The main source of radiation then is the transuranics (uranium, plutonium). Stuff like strontium and other elements would have decayed away.
Correspondingly, the very long half-life material has low level of radiation. (For example the human body has a half-life measured in billions of years - does that mean we are 'unsafe' for a billion years?)
So, if you wait 10,000 years for geology to change and Yucca to actually get rainfall, etc. you'll find in the interim that the level of radiation danger is much reduced. They'll still have plutonium etc. and radiation, but the containers will be not that "hot" at all.
IMHO, the Yucca solution is vastly overengineered and well within what is safe, and the prospective claimed risks to it are not reasonably based on the facts.
In addition to that, it is a highly reactive and toxic heavy metal, even without radioactivity as part of the equation.
The problem is not the small amounts, but a concentration far beyond what would normally occur in nature. It may not take 10,000 years, either, the ice sheets were pretty much gone here in just a couple of thousand.
I agree with the concept that processing spent fuel to get more fuel does address the waste problem--it is the equivalent of recycling.
As I said, I am not against nuclear power. Processing 'spent' fuel currently in questionable storage areas is a good idea--more fuel, less waste to inter. In the short term this is a solution, but it is a remedy, and not a cure.
These are problems which need to be addressed, especially if we are going to expand our capability.