I'd say it depends on the intended use of the device, how long it's required to last between charges, how accessible it is and so on.
Can power be drawn from whatever is being monitored? Is there, say, a 12V dc supply available, or USB power, or a mains socket? Is the battery a must-have, or just a handy feature which some customers won't need at all?
More often than not, when I buy any new device, my heart sinks when I see that I have yet another charger and yet another battery to have to worry about. If I can stick some AA's in a device, then that's great, it's one fewer problem to contend with, and a guarantee that the product won't become useless once the original battery will no longer take a charge - which, inevitably, happens when the device is no longer in production and spares are no longer available (besides the inevitable no-name copies, of course).
On that subject, if anyone can point me towards a genuine spare battery for an Epson P-3000 photo viewer, I'd love to hear from you!