We had this discussion earlier in a QOTD in the Running Thread (
link). There is scientific research that allowing the shoes to "rest" increases the longevity of the shoe's life. Although, these research studies were funded by shoe companies (who do have a vested interest in the outcome of said funded studies). So it's hard to be conclusive one way or another for me. But I think it comes down to this for me, if I have two pairs of shoes I have two options.
A) Rotate the shoes every other
B) Don't rotate the shoes and do back to back
As long as both shoes are equal at the beginning, then even if there is a hint of truth to the science it would be better to choose A for longevity. I'll personally have three pairs in case my rotation gets screwed up. For instance, the plan is Kinvara B for 5k/HM and Kinvara C for 10k/M. I've run the 5k, but now it's clear it is going to rain for the 10k. I break out my 3rd emergency pair (Kinvara A - that's further in distance than I want them for racing) and run the rain 10k in those. Then, I'm still good to go with my two best pairs for the HM/M. The HM/M are way more important for shoes than the other two races in my mind.
Now your original question seemed more prefaced on performance of the shoe. Since you may or may not be concerned with the shoe's longevity but whether you can race a HM/M on consecutive days. I can't remember reading any research from a performance standpoint. The only concern I would have is if the HM is rainy, will you end up having to run in the 5k/10k shoe you planned to avoid rather than the new shoe? I guess in that case you'd probably run the 5k/10k/HM in the old shoe and save the new shoe for the M. You could always give it a small trial run with one of your back to back days. Like the week of 12/11 on your Tues/Wed run. That would be a safe trial option if you'd like to test out how it feels performance wise.