Why aren’t Xbox controllers rechargeable? ?

Actually, the other way around. PS4 controllers annoy me because once the battery runs low, you've got no choice but to plug it into a charger and I don't know if this has changed but mine seems to be pretty picky about which chargers it'll charge from.

With the Xbox controllers you can just swap in a fresh set of AA batteries which takes a few seconds at worst. I keep a couple of sets of rechargables in the charger all the time so I'm not constantly buying batteries either.

The standard controllers weren't wireless, but wireless versions were available.

I have a ps4 and I personally find the hassle of replacing batteries too much. (yes I'm lazy) It's a lot quicker and simpler to just plug in the controller, especially since you can just leave it on rest mode so the controller charges. Over time, I assume the rechargeable battery will degrade but that's a matter for another day. As for your question they probably just want to siphon a few extra dollars from you for an adapter or whatever. 

Because then they wouldn't be able to make extra money by trying to sell you a recharge adaptor kit from the aftermarket accessories range......

I find using rechargeable batteries much better than the old system where you plugged the controller in.  My recharge pack deteriorated too quickly, and XBox parts used to be stupidly expensive.

Also improved is being able to plug a standard mic jack in to them, instead of paying a fortune for stereo

Not sure but there is a $20 2 pack of rechargeable battery packs that you can buy I love them personally.

Because they suck. I guess that is what happens when you get a controller the size of a sega genesis

I like Xbox better, you can buy rechargeable battery packs or just get rechargeable AA's.  You are not forced to plug in and you have options for a quick swap.  

I prefer swappable batteries over recharging.  Over time a recharging battery will degrade in quality and life per charge to the point you will have to have it plugged in to even use it.

Swappable batteries will give you a clean, full charge every time.

It’s better that way. Batteries are easier. You can get rechargeable batteries.