I want to sell you on the 'primitive SIMD regs are truly typeless' point. (which I thought you had already agreed with) :)

Here are some examples of tight interacting between int/float, and interacting ON floats with int operations...

Naturally the examples I present will be wrapped as useful functions in libraries, but the primitive type shouldn't try and make this more annoying by trying to enforce pointless type safety errors like you seem to be suggesting.

In computer graphics it's common to work with float16's, a type not supported by simd units. Pack/Unpack code involved detailed float/int interaction.

You might take a register of floats, then mask the exponent and then perform integer arithmetic on the exponent to shift it into the float16 exponent range... then you will mask the bottom of the mantissa and shift them into place.

Unpacking is same process in reverse.

Other tricks with the float sign bits, making everything negative, by or-ing in 1's into the top bits. or you can gather the signs using various techniques.. useful for identifying the cell in a quad-tree for instance.

Integer manipulation of floats is surprisingly common.