A BUIS is just for EMERGENCY USE, thus any flex or play is inconsequential.
But a PRIMARY SIGHT should be "ideally" on the receiver due to its direct and solid connection to the barrel. I have seen primary sights on a rail and for most self-defense purposes, at close range, I'm sure that would work just fine...
Rmpl
"Our destruction... will be from another quarter. From the inattention of the people to the concerns of their government, from their carelessness and negligence..."
...Daniel Webster, June 1, 1837
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