It definitely would not. The rotation either way is a mixture of up to ~20-30 primitive basic floating point operations, and a few geometric (sin/cos/etc) opera

It definitely would not. The rotation either way is a mixture of up to ~20-30 primitive basic floating point operations, and a few geometric (sin/cos/etc) operations, and you only need to do it in the cases where you're actually going between both systems, and more than once. It's difficult to even ballpark, but it's highly likely that the caching gives anymore than a fraction of a percent of performance boost, like 0.5% or whatever. But now multiply that over hundreds to thousands of similar little 'premature' optimizations.