What's the minimum voltage we could get without intervention? I'm not well-versed in batteries, but I do recall that a typical Li-Ion cell has 3.7V on output, which might be tricky to fit into one AA/AAA, but isn't that far from two AA/AAAs.
While there's no standard way for devices to accept multiple AA/AAAs, to a first approximation, a Li-Ion cell reformatted into a shape of two AAs with ~1-2mm "space" between them, would fit all my remotes and a third of my children's toys - so I could see a "Li-Ion double AA" working as a product, provided it could shed that 0.7V somewhere. The biggest problem would be devices accepting odd number of batteries.
This specific battery is unlikely to work for other devices because the controller has an extra connector, presumably to detect it and control charging (which happens over a USB cable). You'd at least need an XBox controller to charge it.
Some manufacturers also make Li-Ion replacements for multi-AA devices, but thats then specific to manufacturer and device and the exact placement it expects.
I do have devices where the 2xAAs are in a column configuration.
Edit: Replaced remote with devices (it's a keyboard not a remote)