#you end up with clunky kludges as in e.g.:

[silverwhittlingknife]

comics are super-contradictory on what the pit does, but YEAH, i'm 100% with you, OP. it should have bad consequences!!

if you want some of the lazarus pit stories that skew more toward the ominous side, i think some good comics to check out are

batman 243 (first comic to introduce the lazarus pit)

lost days (backstory for jason's resurrection)

resurrection of ra's al-ghul (dick & tim fight over whether tim should experiment to see if he can use the lazarus pit to bring back his loved ones)

I do not care about what canon says, pit "madness" exists to me. Not because I need an excuse for Jason's violence and the murder attempts on his family, but because, from a storytelling point of view, you need your immortality bath water to have some consequences for your heroes to not use it every tuesday. You want death and injuries to still matter, it is silly for your characters to be worried about each others' health when they can just take a dip in the magic green goop and be back in one piece without side effects. Which is literally what is going on now in the comics, with the batkids dying and immediately being resurrected with a sip of the forbidden green smoothie. Like, what's the point than? You're going to tell me the tale of a man who created a symbol from his grief, only to give him some magic goop that can make him and his loved ones immortals without drawbacks, and I'm supposed to believe he would refuse that power? That he would not have dip Jason himself the moment the kid died if there was no consequences? Nuh uh. Like, I can understand a "immortality is against nature" as the simple reason why your heroes would be against using it, BUT when we are talking about a child that was murdered, it's not really immortality to bring him back to life, so it doesn't work.

Immortality must have some aftereffects so your heroes can understand the attraction to its use, but the cons are too much for them to actually do.