> The 80-bit format has an explicit 1, unlike the normal IEEE float and double.
Apparently the explicit 1 made the hardware much simpler, and with 80 bits it doesn't cost you much to have an explicit 1.
(To explain for others: in the normal float format, the first bit of the mantissa is assumed to be a 1, so this bit is not explicitly stored. This gains you a "free" bit of precision. But then you needs special handling for zero and denormalized numbers because the first bit isn't a 1. The 8087 stores numbers internally using the 80 bit format for increased accuracy. The 80 bit format stores the first bit explicitly, whether it is a 0 or 1.)
> The chip has BCD support.
BCD was a big thing in the 1970s; look at all the effort in the 6502 for BCD support, for instance. My hypothesis is that cheap memory killed off the benefit of packing two digits in a byte.
> We got an 80-bit format, but no 16-bit or 128-bit format.
They did a lot of mathematical analysis to decide that 80 bits for the internal number format would result in accurate 64 bit results. Something about losing lots of bits of accuracy during exponentiation, so you want extra bits the size of the exponent.
> Don't we like powers of two?
Looking at old computers has shown me that word sizes that are powers of two are really just a custom, not a necessity. In the olden days, if your missile needed 19 bits of accuracy to hit its target, you'd build a computer with 19 bit words. And if your instruction set fit in 11 bits, you'd use 11 bit instructions. Using bytes and larger powers of two for words became popular after Stretch and the IBM 360, but other sizes work just fine.