There appears to be some RNG involved. I've only encountered 3 leviathans, but all since H&H update.

My experience has gone one end of scale to other -
1- first ever encounter, didn't even know what it was, had to google it afterwards. Luckily didn't die but as I mined the barnacles, got like 6-7 of nodes before it started sinking,

2 - this one I thought was bugged because I literally mined almost every single barnacle on it, until the very last one then it started sinking. I managed to pickaxe that while sinking and swam to boat which I now learned to always park with ladder side facing you if using karve.

3 - this one sank really quick, barely after getting first cluster of 4 barnacles

So while my xp is limited, seems like there is some kinda RNG roll on when it sinks.