First, for systems with regular batteries, get a charger and some rechargeable batteries. It's really easy and solves all of your "but I keep needing to buy batteries" problems. Rechargeable batteries are about as good as regular ones now and last plenty long.
I don't really understand, why are so many people voting for non-removable batteries? Is this your first console generation or something? Because dealing with the problems of a dying non-removable battery are a big problem, and it's one that doesn't exist in anything using standard batteries!
Going with non-removable batteries is going for form over function, since it allows things to be made thinner, but that is a bad tradeoff that hurts systems and controllers significantly in the long run. All of these devices with built-in batteries aren't going to be very usable in the future, while anything which uses regular batteries and still works will be. I already have multiple PS3 controllers that can barely hold a charge, and this isn't a problem that Xbox 360 or Wii controllers have! It's the same on handhelds, the DS and PSP, and their successors, will have problems that no older, AA battery-using handheld could. I have a few original model DSes and their battery lives are pretty bad now, and it'll just get worse in the future. Newer systems like the Vita, 3DS, Wii U (Gamepad and Pro Controller), Switch (particulary the system and pro controller; for joycons this is an issue, though Nintendo sells AA battery handles you can get for joycons, which is a very nice option; they make joycons as thick as a Wiimote and more comfortable too, and are worth getting), and PS4 controllers will all have this problem too. From looking at this thread it's clear many PS4 controllers already get poor battery lives.
And seriously, using batteries doesn't make a controller that much thicker or harder to hold! The X360 and Xbox One controllers are very comfortable and well-designed controllers, and both use batteries. It's disappointing that after the Wii Nintendo stopped caring about this, but at least Microsoft wants their system to be fully playable in the future without needing to rely on maybe somehow managing to find a new unused built-in battery for your old devices online, and then hoping that it actually works as well as an original battery would. Finding good replacement batteries is not easy to say the least, but finding AA or AAA batteries is simple. Just charging up the rechargeables you already have is even simpler.