I believe the easy answer is that they thought they could adapt x86 to all markets, and that became the strategy.
More complicated is that Intel came into the mid-90s with several "next generation" architectures, some that weren't solely developed at Intel. XScale came from Digital and had IP from ARM. i960 was a joint venture with Siemens. And they still had the i860 which by this point it was clear was never going to meet expectations in the market. So when the x86 folks said "Intel should put all it's wood behind our arrow", politically they were fighting groups that were weakened by NIH or who'd already for all practical purposes failed. Probably didn't hurt that Pentium was doing quite good and P6 was looking good on the horizon.
More complicated is that Intel came into the mid-90s with several "next generation" architectures, some that weren't solely developed at Intel. XScale came from Digital and had IP from ARM. i960 was a joint venture with Siemens. And they still had the i860 which by this point it was clear was never going to meet expectations in the market. So when the x86 folks said "Intel should put all it's wood behind our arrow", politically they were fighting groups that were weakened by NIH or who'd already for all practical purposes failed. Probably didn't hurt that Pentium was doing quite good and P6 was looking good on the horizon.