Personally I think that although there is enough evidence that the FPU is physically there in early SX units (and absent in some later chips) I am not so sure it was the way of dealing with broken DX chips.
I believe in 1991 it was simply a good time to have a cheaper 486 product.
I think these two statements contradict eachother somewhat.
Early 486SX CPUs actually did contain the FPU, so they were technically the same die as a 486DX. Which means they weren't cheaper to produce.
Given that they'd also require new motherboards, with an FPU socket, where is the cost saving?
Perhaps the truth is somewhere in the middle:
Intel encountered yield issues with early steppings of 486, mainly in the FPU.
So they introduced a new stepping (ergo CPU identification changed), where they could laser off the FPU if it failed validation.
Eventually, the market changed: more demand for 486SX, but yields also improved, so less 'lasered off' chips available.
So Intel introduced another version of the 486SX, with the FPU physically removed, to reduce cost, and meet market demand for the 486SX.