Assuming that the character's total hit points are significantly larger than the volume of one burst of healing, and significantly larger than the amount of damage the character is likely to take in one turn, that healing can easily be expended in a calculated, stress-free fashion to maximize durability. Those assumptions are often but not always true, given the enormous amount of hit pints D&D characters possess, the way healing is framed, and the relatively trivial by-the-book definition of a "challenging" encounter. If they are false, then yes, the world with self-healing gets more swingy.
Maybe it's because I run for seven players, so there are 140% of the "normal" number of monsters who can area effect/focus fire, but I find the amount of damage that can be incoming to a character in one turn is pretty high. Couple that with several nice bonuses that certain powers can grant for being bloodied, and we get quite a few heart-in-mouth moments.
YMMV, but I'm just speaking from a personal experience perspective.
I'd really rather guaranteed encounter-based healing was an option rather than mandatory. I think feeling overwhelmed means the players are probably overwhelmed unless they know better. As the example shows the game isn't actually overwhelming the PCs because the opponents are too difficult, rather the PCs are facing a beatable opponent where they can win most of the time.
In pretty much any challenge-based RPG, the characters have to face beatable (or escapable) opponents. If the chance of surviving even each level is ~50%, grinding through the ~1000 characters you'd need to get one to level 10 would be a real chore.
They simply must heal each other during combat to do so. This puts healing front and center as an important part of combat every combat. I don't think it necessarily needs to be. Healing used to be a resource tracked on a much longer timeline. That should also be an option again.
Again, I can only say what I have experienced, but I find that is situational. The most important thing deciding whether healing will be an "essential tactical component" in 4e is whether or not the characters manage to take control of the encounter circumstances. To seize the initiative in a non-system sense.
The other weekend, we had two combats particularly that were nominally the same level, but played out very differently. In the first encounter, the characters scouted out successfully, correctly assessed the situation going in and managed to gain surprise. The result was a real blow-through, for the party. I don't think any in-combat healing was used (although a few surges were spent in the ensuing short rest) and the monsters were hardly given a chance to apply their strength.
The second encounter was totally different. The party walked in hoping to negotiate when a previous encounter had ensured that this would be a throwdown. They got bounced, and only just scraped out without loss. Given the start they got, they actually did really well - but they still got hit pretty hard. And in this combat, yes - in-combat healing was a major "feature"...
Ultimately it's probably a matter of taste, something along the lines of tactical vs. strategic play.
Again - personal preference, but I find 4e does both. Hit points = tactical, healing surges = strategic.