I would be pretty curious about such a system. Or, maybe more practically, it might be interesting to have a system pretends the L3 cache is ram, and the ram is the hard drive (in particular, ram could disguise itself as the swap partition, to so the OS would treat is as basically a chunk of ram that it would rather not use).
Intel has such a CPU with the previous gen called the xeon AMX with up to 64gb of HBM on chip. It could use it a cache or just memory.
Philip Machanick's RAMpage! (ca. 2000)
> The RAMpage memory hierarchy is an alternative to a conventional cache-based hierarchy, in which the lowest-level cache is managed as a paged memory, and DRAM becomes a paging device.