So, arenas without address space reuse. Let's say you allocate 1 GB/s (conservative with dozens of cores), and use a regular 48 bit address space, split 1:1. You'd run out of bits after 2^47 / 2^30 = 128K seconds, or 36.4 hours?!
You could get 9 more bits, but they're not free…
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If the allocations are smaller than page size and have varying lifetimes, memory usage would become a huge problem too. Single long-lived 16 byte allocation will hold onto a 4k / 16k page and the page tables for it. Sparse address space use is also not at all free either.