Why wouldn't have the F35 a pilot in it?
Current fighters are built around the size and limitations of a human being. The larger ones are also designed around the size of radar that will be in their nose, but pilotless aircraft might operate in swarms with the radar function offloaded. Get rid of the pilot and you can make cheaper, lighter, stealthier planes that work at stresses no human could cope with.
It's a surprisingly cheap aircraft, even if it doesn't look that way. It's cheaper than upgrading the F16s and 18s to today's standard. It's cheaper than it would be to make those today alone, excluding the upgrades. And then you have a plane without integrated systems.
And it's designed to replace half a dozen planes, no wonder it has to be versatile. It's like the MBT, which replaced every other tank on the field. It's cheaper to have just one type. And for other roles there are UAVs, AC130s and AWACs.
Besides, I'm like 90% sure it could fly without pilot, either already or with future upgrades.