Re: Would the Ikkyo pin work in MMA?
It would be a rare circumstance for a cop to perform a shooting-type takedown, and exactly because of the reasons you cite. We really prefer to remain on our feet and use the cool tools we are issued; baton, OC spray, TASER. An old joke is that they are "like birth control pills - they take the worry out of being close."
Where grappling/BJJ plays a role is when the officer loses his feet for whatever reason. It is superior to have a ground game when you need it.
A variation of ikkyo is taught, at least out here in California, as a "single arm takedown" in the academies. It works usually, but isn't a pretty as on the mat, and primarily because the officers don't get anything near enough repetitions in training to make it really effective. Most simply rely on their own sobriety, strength and size to make it work.
I suspect that an ikkyo in a cagefight would look very similar to the single arm takedown technique.