Well if anything this thread has shown me to never underestimate the variety of ways people use their consoles. If you had told me with a straight face that you use a corded controller to play console games I would have never in a million years believed it. In fact I would have laughed assuming it was a joke. Yet here we are in 2014 and people apparently are indeed doing it. It blows my mind, but there it is. I guess you just never know. Same with choice of built in battery, I always viewed that as a heavy negative on the psx controller side yet others see it as a positive. Once again something I never expected and still don't get it but it is what it is. I'm just glad very few devices force that on us, I just imagine what if my power tools ran out of battery power and rather than just swap the battery like I do now, imagine if I had to then find a 15 foot cable and plug the tool in to keep working. Stranger yet, imagine some people found that to be a positive! I don't know, I'll just bin this in the I Really Don't Get It file and move on because, well, I really never will understand it so why waste any more cycles on it.
I always saw it as a positive, or a feature, when a wireless device has a built in battery. For example, I've seen many portable audio devices where the higher-end models have built in batteries and the lower-end models use standard batteries. Or wireless mice/keyboards. Has anyone honestly seen a higher-end model have user replaceable batteries, but the lower-end model had a built in battery? I can honestly say that I haven't.
Power tools (or any other power hungry devices) are another story. You can easily go through a full charge in a workday, whereas it is difficult to go through a full charge on a controller in one sitting.
More and more cellphones are sealing the case / making the battery non-user replaceable. Samsung is one of the only big phone makers that consistently makes the battery user replaceable. LG, Apple, Sony, HTC and Motorola all have non-user replaceable batteries in their flagship phones. Even the higher-end Nokia phones (not very familiar with Nokia, dunno what their flagship phone is ATM).
The -ONLY- issue with built in batteries, is that they're non-user replaceable for when they do eventually die, but that shouldn't and usually doesn't happen for several years. There's a good chance that something else will stop working by the time the battery stops holding a charge.
Microsoft's battery situation is more versatile, but comes at an additional cost. I feel Sony's battery situation is more modern and (IMO) more convenient (vs using standard batteries), with the downside being that it's not user replaceable.
dobwal's post pretty much sums it up. Different strokes for different folks. I also doubt anyone here would make a console purchase decision based on the batteries in the controller. Some people are just blowing things way out of proportion.