The advantage I experience with 'coin cell' batteries is that they will maintain their full 3 Volts throughout their lifespan.
This can greatly exceed ten years in some applications, like my garage door openers.
I have a counter top kitchen scale, used a lot and it eats those 2032's, but far outlasts the older scale which takes a ($) 9 Volt ($) and the coin cell is far easier to replace as well (the Nine Volts like to destroy their connector, then you're soldering in a replacement).
Each scale has its advantages, but the newer ($9 Amazon Scale) gets ten times the usage. I also keep a 25 year old person scale by the fridge. Came with Lithium Power and no way to see or replace its battery and it is used once every day, looks like you would be bending steel to find a battery you'd need to solder in, if you could get Alibaba to get you a replacement. I'll just get another scale.
Six months was about the life of the flat remote's batteries and I buy them on a nine cell card at Ace Hardware for $1.50. You can find them cheaper on Amazon (but I'm leery of cheap batteries) and you certainly don't need to spend $3+ each at the drugstore. Since they give up without much warning, I have spares on hand. I've never had any leakage from 'coin cells', but lost use of remotes after their AAA's leaked. And that leakage occurred while those remotes still had working juice from the leaking battery.
I've never had any problem changing them, you need a tool (like a round toothpick or corkboard tack) to open the flat remote's battery compartment and don't bend those springs. The enhanced remote needs a sharp, straight edge to slide battery door off.
But either 'latch effect' beats most remotes where the battery compartment flies open on its own and ejects battery's and cover into hiding.
What I meant last week about enhanced's first month on brand new Duracell's was just that its IR Blast was noticeably weaker, still works fine (if you 'point' more carefully, but I do like the point anywhere
with strong batteries) and I'll not change batteries until the [off/on] red light starts blinking. I shall report lifespan then (the two pair included with DVR+'s from CM lasted two months each to completely dead) With the flat remote, it's full power until perceptible dimming of its red light.
After I've used most of my Costco card of AAA's, I'll look into getting it some Lithium AAA's and see how long they last, I'm sure they'd do 'IR' better.