One really good reason for standardization is for your Go Bag. You don't want to have to carry all kinds of batteries on your back.

Note that manufacturer's stated runtimes are for alkaline batteries. You can get up to nine times (9X) the runtime using lithium batteries (the non-rechargeable kind). Lithiums come in lower rated forms (I have seen 4x, 6x, and 8x), but I would avoid them. Lithiums also have a ten year shelf-life, don't leak, and work in colder temperatures. In an emergency you don't want to find out that your batteries are dead (including your spares) because of the shelf-life, or that they have leaked and ruined your device.

I have standardized on AAAs and I only use lithium 9Xs. I mainly picked AAAs because I wanted a really small EDC flashlight and I found a excellent one that uses a single AAA (Fenix E01). I also wanted batteries that would be easier to find in a pinch.

In my Go Bag, I have a 3 AAA multi-mode flashlight (Nebo Redline) and a tiny 2 AAA radio (Kaito). I don't have a AAA headlamp yet, but do plan to get one. There are lots of AAA ones to choose from.