For me, I'll always choose a device with standard, user-replaceable batteries over a built-in battery.

1) If the device battery is dead, I can swap it out in seconds and be up and running immediately.

2) Built-in batteries fail, and replacing them ranges from difficult to near-impossible and often involves damaging the device's casing to get the built-in battery out.

When I'm spending $100 on a computer mouse, I'd really like it to last longer than the life of the battery and not have to destroy the casing to get to the battery to replace it.

IMHO Sony nailed this pretty perfectly 30 years ago on devices like the Discman: Have a footprint which can support a number of standard batteri(es), but engineer it so it also accepts and detects a specially-designed NiMH pack. When the special batery is present, allow the battery to be charged anytime external power is provided.

Now you have the best of both worlds: Economical rechargable use for the 90% of the time that the user's in their normal routine, and easily ability to swap temporarily to universally-available alkalines in exceptional situations.

Note: When I had one of these, I just used my own NiMH AAs and jammed a folded-up piece of cardstock against the detection switch, which worked perfectly fine.

Regarding #2 the fact that probably the majority of battery-powered non-toy devices now are designed not to ever have their battery serviced is indicative of a (in my opinion) diseased mindset of disposability. Each of the components including battery and other wear parts are only spec'd to last about 12-18 months. We're being conditioned (by one-year warranties and by the lack of repairability) to think that it's normal and expected that you discard and replace everything smaller than a car every 18-36 months, and a car every 7 years or so because "obviously" anything older than these milestones is "obsolete anyway."

Yeah. Though to be fair, the alternative in the controller space in that era was hot-swappable rechargeable battery packs - a ton of 3rd parties provided them for Xbox 360 controllers.