It should be noted that 4e did have a few ways in which to heal without using surges – notably, cure light wounds (heals someone as if they had spent a healing surge), cure serious wounds (heals as if they spent two healing surges), and mass cure light wounds (heals all allies in 25 ft as if they spent a healing surge plus your Charisma modifier). These were all daily powers, so if you were a cleric you could specialize in healing and get a little more oomph, but there were still limits.
Another good thing about healing surges and the accompanying healing powers various leader classes had was that they leveled the playing field. Being able to heal twice per encounter (thrice at high levels) with a small bonus to the heal was the baseline for leader classes. With some minor changes, that was the same for the cleric's healing word, the warlord's inspiring word, the bard's majestic word, and the shaman's healing spirit. The artificer's healing infusion worked slightly differently in that it healed without spending a healing surge, but in order to recover the use of it on a short rest someone needed to spend one (which seems like a big power increase, as it allows you to spread out surge use over the whole party even if only one PC is getting the beatdown). The result was that multiple classes could fill the healer role, and you could easily have a fully functional party without a cleric.
It's also a good idea to consider the reason for the healing surge mechanic: the ubiquitous use of wands of cure light wounds in 3e. In 3e, it was assumed that you could easily acquire or create magic items if you had the gold, and a wand of cure light wounds was dirt cheap: 750 gp for 50 charges that each healed 1d8+1 hp (as a comparison, a 4-person party was expected to find a total of 4,000 gp worth of treasure before level 2, and 77,000 gp fron level 10 to 11). 3e was balanced around the assumption that a party would have about 4 encounters per day, with each encounter being relatively easy on its own but sapping some resources in the form of hit points and spells expended, so by the time you got to the fourth encounter you actually had some danger. But the healing stick broke that, because it made it easy to bring everyone back to full hp between fights.
This, in turn, lead to adventure designers filling adventures with harder encounters to provide a challenge. In many cases this lead to fun encounters where players felt like they were actually fighting for their lives, but it also encouraged casters to go nova with all their spells. This in turn forced groups to retreat because the casters were spent. Another side effect was that since the cleric was designed with the assumption that they would spend a significant amount of their daily resources healing people, the rest of their spells were quite powerful. But when they no longer needed to use their own spells for healing, it freed them to use them for all sorts of powerful buff spells and other powerful magic, making the class extremely powerful.
So in 4e, they made being healed the daily resource, not healing someone. So now you could both have fun, challenging encounters and have an attrition mechanic. Now, I'm completely on-board with the complaints that fights dragged on too long and maybe allowed too much healing – those are valid complaints. But to me, that's a question of calibration, not concept.
