In Torchbearer 2e, which has been most of my RPGing for the past couple of years, PCs can't die unless death is explicitly on the line - either (i) because the PCs are in a kill conflict, or (ii) because a PC is sick or injured (these are both technical conditions that can be acquired by failing a test or losing a contest) and the GM announces that "death is on the line" as a possible consequence of a failed test.
If a PC does die, then provided they have one unspent Persona point (a type of "currency" that players can accrue via play), the player can spend the Persona and declare that the PC has "the will to live". This then triggers a set of rules, in which the player and the GM both have decisions to make about changes to the PC sheet, and which also require the player to explain how their PC miraculously survived.
In 20 sessions of play, we have had one PC "die" twice and another once. One all three occasions, they had the will to live.
None of this stops the play of the game being intense. When my players initiate combat, generally it is to capture or to drive off (rather than to kill), because they don't want death to be on the line. Those combats are not less intense because the PCs aren't at risk of death.
As I already mentioned upthread, another RPG I've played in the past little while is Prince Valiant. It's default approach to stakes is that death is not on the line. Only if the fiction makes death the only real stakes (eg someone has been hurled over the parapet of a high tower; or someone is lying injured on a desert battlefield, bleeding and without water) does it come into play as a possibility. This doesn't stop conflicts, including combats, being intense.
I don't think that intense and engaged play requires making players think that death is on the line if it is not.