Ressurection is hard

It is no longer possible to revive an individual through spellcasting alone. Revivify, Raise Dead, Reincarnate, Resurrection, and True Resurrection can no longer be learned. There are still three ways to return an individual to life:

• Petition the Gods. This method would likely involve traveling to or otherwise negotiating with whoever the soul belongs to, possibly demanding of you to give up something of equal value. There is no guarantee of course that the souls owner would even want to meet with the PCs let alone give up the soul even if they do.
• Steal the Soul. This is by far the most perilous method and demands of the PCs to find a way to take the soul from its owner by force, a course of action that is certain to anger said owner and likely to create endless problems for the PCs long after any successful attempt. This would require the PCs to travel to the souls destination in the afterlife, locate that soul, and convince that soul to leave its afterlife with the PCs (a non-trivial task since most souls lose their memories in the afterlife), then find a way to lead it out of that afterlife - an initiative likely to receive intense resistance from the souls owner. Finally taking the soul back to the mortal world will turn it into a ghost, allowing it to find an body for to inhabit.
• Wish. The spell Wish can recall a willing soul to an body provided one already exists for it to enter. Such usage of the spell is likely to have intense side effects, for the return of a being to life is of no small significance, and could possibly bring consequences far beyond the initial effects of the spell depending on the owner of the soul's reaction to such an event. The description of the Wish spell applies.

Death is not Trivial

Since returning from death is no longer trivial, it makes sense that death is no longer trivial also. When rolling death saving throws you now add your CON modifier to the roll. You must succeed on three death saving throws before you fail five in order to be stabilized. Rolling a crit or crit-fail on a death saving throw counts as two successes or failures respectively.

Anyone may attempt a DC 10 medicine check to instantly stabilize a creature. If an unconscious creature is healed, they regain consciousness and gain a level of exhaustion. Creatures with any levels of exhaustion cannot regain consciousness through being healed.

Staying Up

Not every PC has to die by bleeding out on the floor of a dungeon. When a character is reduced to 0 HP, if they have no previous exhaustion they may choose to stay conscious, immediately acquiring one level of exhaustion instead of going down. A character in such a state makes a death saving throw at the start of their turn as normal, but may act on their initiative. Incurring damage still causes them to automatically fail death saves and they cannot be stabilized except through magical healing or by succeeding on 3 death saving throws at which point the character gains 1 HP. In this state a character dies when they fail 3 death saving throws.