Think of the average consumer here, not the crypto-electro-engineer in her microcomputer lab.
Why choose?
I'd agree, but OP is looking to make a choice for a website.
You're evading the question. OP has already gathered the information they sought and has settled on "satoshi".
Again, why do you choose between alienating "common people" (with "μBTC = microbitcoins") and alienating "crypto-electro-engineers" (with "bits") when you can accommodate both so easily with "mikes"?
I didn't mean to evade the question; no sinister intent or ulterior motive - just noting the fact that there was a poll asking for a choice to be made. That was 'why choose'. Otherwise I tend to the anarchic over the dictatorial.
I'm advocating an easy to use system for general use by people, one without the psychological high price barrier, one that might help bridge the adoption chasm, but if some folk decide to stick with SI good on them, that's their choice, and I'm sure there will be situations where it will be necessary to use SI, just as there'll be crossover between the groups; sometimes SI may be more appropriate, other times, bits.
I confess I don't know what the 'mikes' solution is, maybe you can explain? Maybe mikes will become another widely used option, and maybe there'll be more options we haven't thought of yet, each offering advantages in certain situations, for certain groups of users; for example, SI would be a good choice for backend IoT transactions; bits for the aforementioned coffee shop example.