I would be perfectly ok if I was trying to see a copy of a web page from five years ago, and it said that I had to make a request and it would be available in five or ten minutes.
I think I could wait five or ten minutes for a web page to get pulled from the archives.
A problem with most forms of warm storage is that they involve moving media around, which itself can lead to degradation.
I would like to see some write-one and really last forever form of storage to come into widespread use. That seems ... like it's still a few years off.
And you still have the issue of how such storage is read, and how that affects total lifetime.
In that case if the low-demand data front-end machines get too much load, you'd be entering a queue to be served.
Not sure that's realistic here though, it sounds like the main problem is just the volume of data so whether the storage for the data is hot, warm or cold isn't necessarily going to make a big difference and having enough frontends to serve the content isn't a big problem (in comparison) either