The idea with really cheap batteries is that they don't need good energy density. You just swap them every so often and put the one you aren't using in the charging rack. You could even carry your own reserve energy with you!
Most modern devices have an integrated 3.7v Lithium battery so standardisation should be possible but I see no market forces for this - devices with short lifespan (limited by a non-replaceable battery) are more profitable.
But please don't exactly match AA/AAA sizes. That will cause much more harm than good.
I don't think the technical difficulties are the problem here.
We might eventually get back there; maybe the EU will do for e.g. hand tool batteries what they have done for phone chargers and mandate an interchangeable standard.