To me, I have the opposite view.
Save or die is boring. Fail and done is not tense, not dramatic- it just leads to someone out.
Save or held, save or fear, save or - insert significant impact that drives action - is an event where fsilure leadsvto events and needs right there in combat.
I agree. That wisdom save vs charm when you're fighting a vampire? Hugely tense. Even a DEX save to avoid a huge fall can be pretty dramatic, particularly if the consequences are more than just the damage: Just last weekend we were fighting a green dragon, who had dived into a lake. Cleric empties out the lake with control water. My rogue skis down the side of the lake onto the dragon's back, passing an Acrobatics check to hang on. Dragon flies 80' in the air taking me and the barbarian with it, and uses a legendary action to try to knock us prone. DEX saves to avoid falling 80' all the way to the bottom of the lake... We'd worked hard to get into that position! It was a dramatic moment. I failed, the barbarian succeeded (remembered later that I should have had advantage as I was Hasted... dang it... but neither here nor there).
It was a major setback that we nonetheless overcame that lent drama to the scene in a way that rolling a save to not instantly die would not have.
Same campaign about a year ago, we ran into a pair of banshees. When the first banshee used their wail, we didn't know what to expect (we didn't know what it was yet), and about half of us failed, going unconscious. Fortunately the cleric saved, and brought everyone up with a Mass Healing Word. The second banshee uses its wail: everyone make a CON save... Now that we knew what would happen, it was terrifying! This time, only the lore bard succeeds, but he'd failed the first time so was likely to go down if he got hit. He gets one chance to cast a spell before very likely going down too, resulting in a TPK. He brings up the cleric with Healing Word. Cleric heals the rest of us, and we defeat the banshee.
Tell me that second CON save wasn't more dramatic than an old-style save or die.