There are lots of little annoyances the battery can help overcome, it's a matter of preference really; lots of pros and cons in the big picture though, from convenience, right down to our environment and resources.(I'll skip that, and save the good for last, so here comes the "blast"...
A cord ensures I run a train, not ever waiting on a charger, I know that's annoying from dealing with RC in the past.... or not, because it wasn't charged. And that's super annoying when you want to have fun NOW. Tools or toys it doesn't matter, I buy just about everything I can on this basis: cords before battery.
Oh, emergency flashlights! But there are my oil and gas lamps to back those up too 
So at each display, it will require attention by an employee about 3-6 times a day when new, increasing over time...? If you do go that route, try powering enough track to keep the battery at, or very near full charge all day, all night. Some insurance policies may not like overnight changing fyi. (Though every EXIT sign does it, lol)
You will still need to clean wheels and track unless you like derailing. The batteries slow it some, but dust still goes from us to the air to the rails to the wheels to the Q tip.
I don't get how a phone controller is better than any other controller, it fully escapes me, and though I think on it, it always come up a downgrade. With a separate controller I can use my phone and run trains at the same time, and never need to look down at the screen to ensure my finger is on a control because on a normal remote, I can feel the controls. (And fyi touch screens don't work well for everyone's skin, I needed an assistant to work on cash registers, and can't dial my own phone sometimes today on a month old device). And how about the device charging! Break out an extra dedicated charger and two more devices. (In Use , charging, & a backup too).
Interesting, but not a game changer imo. Nor is the idea totally new, you'll find lots of threads here on both BT and batteries. Freerails site is all about battery and RC too fyi.
But if it really appeals to you on a personal level, go for it and have a blast. That's why we do this. Tough job, but win me over too.
Personally, I just don't see the fascination with a device controller at home. (I also only see command control remotes as a way to troubleshoot with throttle in hand trackside...old schools fine and sounds annoy me after a bit anyhow)
I do see a way to be highly guest interactive by BT, though I'm not appealed by it, or know if it is being done just yet. But if a guest wanted to, a timed BT connection to THEIR phone to control (any) display would grab interest and build rep. I'm sure.
In fact the concept combined with common ads and data mining (cookies etc.) could be another income base.
One day they'll pry my dead fingers off the handle of one of my Lionel transformers....I hope. (All built before I was too )
