for the unaware: minecraft has something called a mob cap, which is the maximum amount of mobs that a world can naturally have at any given time*. in vanilla minecraft, the mob cap for hostile mobs (creepers, zombies, endermen, etc) is 70 per player - meaning in a single player world it's 70, on a server with two others it's 210, and so on**.
now, this mob cap can be filled up by mobs anywhere, as long as they are loaded and don't have some sort of "persistence" (like a name tag or holding an item) that prevents them from despawning***. in the daytime, this mob cap is usually taken up almost entirely by mobs in caves deep underground. sometimes you'll get a few leftover creepers or spiders from the night before but it's almost always caves, and when the game can spawn new mobs it'll spawn them there.
...however in the night time, mobs can spawn on the unlit surface as well. and since the mob cap doesn't particularly care about where in loading range mobs are, this actually results in less mobs in caves since there are more on the surface taking up the mob cap... meaning in terms of potential mob encounters, it's safer to mine at night.
and game mechanics aside, it's just more convenient to mine at night anyways! if you're just starting a new world, nighttime is nasty. most players want to stay inside and do indoor tasks in a nice, safe base while the monsters roam outside. and if your mineshaft is in your base, it's more convenient to head to the relative safety of the mines as the sun goes down, then come back up to explore the surface in the daytime when the sun is bright and the monsters are few.
so yeah, the ancient songs are wrong. they've always been wrong. mine at night!
*there are some exceptions, like phantoms and mobs spawned artificially or from spawners, that don't respect the mob cap. you can easily have more than 70 mobs on a single player world through spawn eggs, the game just wont spawn more naturally
**each dimension has its own mobcap, so if you have 3 players across 3 dimensions each will have a cap of just 70
***once again, there are exceptions - shulkers, wardens, and zombified/witch-ified villagers count towards the mob cap but are persistent. they are used to make mob switches, which are devices that prevent any further mob spawns from happening when activated.
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