In addition to what others pointed out, storage is also the area that scales best from economies of scale - a single huge facility will have significantly less external heat to contend with, due to a smaller surface area, and thus significantly cheaper costs.

In addition, real-estate costs themselves tend to drop due to economies of scale, and as you grow large enough you can probably set up large remote storage facilities well outside of urban areas, and simply have smaller facilities locally that do a "preserve and ship".

The funding Alcor does also produces twice as much interest as is required to beat inflation, so there's a good margin of error even if inflation rises.

There are certainly risks, but if you had the sort of social buy-in required to spend 0.5% of the world GDP on this sort of project, I think inflation would be the least of your concerns. Natural disasters, major warfare, and severe economic collapses are much more likely to be risks, and unfortunately those are not trivial to mitigate.