Take your pick. Either it’s a rechargable (and you have to charge it – but you certainly could use rechargables to power the booster box), or it’s a disposable and you buy it at need. Or, with some of the newer battery technologies, you can buy precharged rechargables … but it’s still easier to drop those into a booster than to come up with a universal design for a battery when the needs – and the tradeoffs – of devices are so different.
You’re never going to get a perfect solution. As batteries become better, devices will be redesigned around the new capabilities and all that will happen is that the tradeoff points move, not that they cease to exist.