Well, the more I am reading people talking about healing surges, the more I am inclined to think I wouldn't like them. I mean 5E is far from perfect, and frankly I've never liked the rapid healing of 5E by design, but healing surges seem like they would expound that issue with regaining 1/4 maximum hp per use. With roughly 8-10 healing surges a day, you are basically boosting your potential HP pool (in total) by 200-250%, as where 5E is (using say half your HD) a boost of 50% daily.
4e character's "health" was in their healing surges. HP was just what it would take them out of this fight.
In 4e, magic can enhance your health, not replace it.
In almost every other edition of D&D, healing that a single healer can do is ridiculously larger than the HP any warrior can have. In general, adding a healer is a better way to increase your teams HP pool than adding a tough PC.
4e breaks this. Because healing just augments your natural toughness, instead of replacing it, having more "tough" PCs actually makes your team tougher. Adding more healers doesn't do this
as much as adding more tough PCs.
Healer healing is
more efficient than natural healing, but it is also a limited resource. So more healers give you more of that limited resource. Healer healing also gives you access to more healing in a fight, while natural healing occurs between fights mostly.
4e heals are large, even at low levels. Two heals brings back someone almost KO'd to full HP. You have a limited number you can use in a fight however, so you use them strategically.
Ideally, the front-line tough fighter gets modestly focused, and when the enemy scores a lucky blow you keep them up. Alternatively, when the enemy collapses your flank and threatens your wizard, you drop a heal on them to buy time for your warriors to protect the wizard (or for the wizard to protect themselves).
...
Because your in-combat HP are relatively smaller than your adventuring day total HP pool, fights are more threatening even if they don't exhaust you for the adventuring day. You are always an unlucky round or two away from being knocked out. Fragile characters even moreso; they have lower AC, fewer defensive abilities, and significantly less HP.
A tough warrior type will usually have more AC, and ways to generate temporary HP or mitigate damage, more HP, and often a few in-combat "self heals" for tough scrapes. Instead of 2 rounds from being in the dirt, they are 3 unlucky rounds from being in the dirt.
Then, after the fight, everyone cleans up and is ready for another one.
4e combat structure is also built to enhance that stress. Early in a fight, players have limited "extra oomph" resources, while monsters have more numbers. This places a lot of tactical stress on the PCs; if all 5 orcs focus on the wizard, the wizard could drop right away.
Then the players unleash hell, an orc or two drops, and the tactical situation switches. The players "snatch victory from the jaws of defeat" with huge regularity; an "even" fight almost always looks like the PCs are in trouble early on, then the PCs come from behind.
4e's major flaws includes that they didn't do enough to trim the per-turn action economy of monsters and players. So the game could drag on; even a 5 round fight could take far far too long, as each player is doing tactical positioning, using suites of tricks, and reacting on their off-turn.
And when every fight feels like a nailbiter, eventually you get used to it, and they don't feel like nailbiters anymore.