we may be in so different diving environments that it also causes different needs in equipment configuration.
Here it is very normal to use a bit more powerful lights between 2000 and 5000 lumens as a primary light if the diver only has budget for it. not only tech stuff but for normal rec diving as well. usually this means some sort of canister light as a primary and the backup may be some kind of flashlight style torch or two in something like 250-500lumen range. this has to do with the murky waters and overall lower light levels underwater, one may very well need a light even in daylight if diving deep enough (this may not be deeper than something like 10 meters in some situations).
my 800 lumen primary is considered small power here which is why I am planning updating it to a canister light later when I get the funds and will do slightly longer dives
if a normal battery goes flat or leaks it is easy to recognise and one will test the light before the dive by turning it on anyway so it would show if there would be a dead battery in it
It is pretty normal here to have no ambient light at depth, even on daytime dives. The local quarry often has a very thick turbid layer in the 8 - 10m depth range. But, a 1000 lumen light (nominal) is more than adequate.
Regardless, if your primary is a can, I don't see what that has to do with whether a backup has a rechargeable or not.
The issue is not so much whether a normal battery is dead or has leaked. It is if you can tell that it has dropped to only, say 20% charge left. If you are checking by turning it on briefly, just before the start of the dive, how do you know whether it's full or at 20%? Do you really put a meter on the battery (or batteries) from your backup light before every dive day (or trip)? It seems safer, to me, to just put in a battery that is of known quality and known to be at full capacity.
Anyway, I reckon neither of us is going to change our mind about these things, so you do you. As my grandmother used to tell me (often), that's why there's chocolate and vanilla.