What do you mean by doing the math? If you repeatedly sample n_active experts out of n_total, why wouldn't you expect to get some meaningful probability of reuse/overlap once your batch grows past size 5 or so (for the sparsest MoE models in common use)? And you only need enough reuse to fill the compute headroom which is quite small on consumer platforms (we won't have huge TOPS numbers for the typical integrated GPU in Strix Halo or even the upcoming RTX Spark). Plus if you're a single user running multiple streams in parallel the choice of experts will be highly biased leading to more reuse.
There's been some very rough experiments with batching on Apple Silicon (and that's not a highly suitable platform since the compute/thermals bottleneck hits sooner than elsewhere) that seem to be broadly consistent with what I argued, showing as much as 2x total decode throughput with an 8-wide batch. That's substantial in this context.
Assuming you magically use all 128GiB of xRAM you need to read ~32GiB per token in batched mode. On a good SSD that would be 1/3 tokens per second. Cool, 2x that you can do 2/3 tokens per second. Let's assume you are lucky and can actually do 6/7 tokens per second. That's still an extremely far cry from 20+ tokens per second of 27B before any batching.
