"non battery powered wiimotes" would mean you'd need a cord for the tablet (which isn't a Wiimote at all =P). And considering motion controls still exist to a degree, that'd be a disaster waiting to happen. I can see countless people tripping over their own wires or ripping their console off of where it sits. Nintendo'd be too busy with unfair lawsuits to fix this problem with wireless tablets, lol.
... Sadly, I can see myself doing that. I'm a clumsy bastard.
Oh, and protip: rechargeable batteries indeed. Better for the environment, a ton of money saved through gas money spent on going to a store to buy non-rechargeables, and the fact it's cheaper to recharge your own than to buy new packages of 'em regardless of said gas money. Using rechargeable batteries is a win-win for everyone.