Are you speaking from experience with 5E, or analysis of 5E rules, or are you just assuming? Where do you get this idea that a cleric is "expected" in 5E and that a party is dysfunctional without it?
I'm speaking from playing. I've been playing since the PHB was released, and I played in various iterations of the playtest. I don't claim to be the greatest 5e guru, but I know the system perfectly well in terms of the player side certainly.
I don't see it anywhere in the rules structure. On the contrary, I see healing or self-healing built into a number of classes including the Fighter, Bard, Paladin, Fiend Warlock, Abjuror Wizard, and anyone who takes the Healer and/or Inspirating Leader feats, in a way which makes it clear that "playing without a cleric should work" is a design consideration. I also see that clerical healing is pretty inefficient.
I have no idea why you would call clerical healing 'inefficient'. Quite the contrary it is quite efficient, especially if you pick the correct domain, which gives you a significant extra bonus to heals and a CD-based heal. Yes, paladins can heal somewhat, and various classes have some very limited ability to do some self healing, but a cleric offers a much larger hit point reserve that can be deployed to whomever needs it and is pretty easy to use.
I don't see it anywhere in play. You baldly assert that a group without a cleric will be underpowered, but since I habitually let my players tackle challenges which weigh as between Deadly and Deadly x10 on the DMG scale, it seems quite odd for you to be telling me that they're dysfunctional and under-powered by that lack, with drastically reduced survivability. In short, you're wrong about clerics being mandatory. They're one way to survive but not the only and best way, and they have an opportunity cost. I'm not one of those idiots who trumpets "actual game experience" over analysis, because they're actually complementary--but having run lots of extremely deadly fights against unoptimized PCs run by non-powergaming players with only moderately brilliant tactics, and having seen the players win most of these fights (due partly to luck--we've come one die roll away from disaster more times than I can easily enumerate, and as a DM I'm often flabberghasted how improbably few deaths have occurred), I am quite sanguine that cleric-less parties are perfectly viable and fun in 5E, even for non-brilliant players.
Well, I would just point out that it is tautological that a challenge which is passed without any failure by a group isn't the most deadly possible challenge! Either that or your description of your group is drastically underestimating their tactical acumen and game knowledge.
But you're not entirely wrong:
It's good to have a healer in the party, and when I build my own parties I like to have a paladin and a bard so they can heal each other if necessary, but you haven't yet elucidated the utility of the healer in 5E so I'll do it for you: a healer is for reversing high single-target damage so you can either win the fight or continue adventuring, depending on the situation, without bottlenecking on a single character's HP. Without a healer, you can't afford to lose 60 HP to a bunch of fire trolls before taking on an Adult Blue Dragon, because you don't want to take on that dragon when any PC is only 30 HP away from death. If everybody is down 30 HP each the presence of a healer becomes a non-issue since you can't continue anyway without resting first, but a healer lets you smooth out spikes. But there's an opportunity cost. During combat with the dragon, a healer can (but doesn't have to) spend his action to reverse some of that 70 HP of damage that the dragon just inflicted on you, and that may or may not be better than having another Sharpshooter dealing 50 HP right back to the dragon. Healing you lets the other party members have more time to kill the dragon; so does Polymorphing you into a tyrannosaur instead of healing you. If you can arrange to have a healer in the party without giving up anything else important (e.g. a paladin/sorc can cover tank/summoner/melee/counterspeller/healer roles easily, or a Lore bardlock could do healer/ranged damage/defense/summoner/skill monkey) it is certainly worth adding that capability to your repertoire. But everything has an opportunity cost, and playing without a cleric or even a healer is valid and can be fun and effective.
No need to explain tactical concepts to me, I've written wargames, and am pretty adept. Try challenging me to a Star Fleet Battles game some day, just don't bet on winning
I understand what you're trying to say. However self-healing doesn't help with the focusing healing where it is needed, when it is needed. A cleric, again particularly a healing build, can focus quite a LOT of healing on a character when its needed. Beyond that he can bring people back up, which self-healing cannot do, and that is the most critically useful function of all.
Yes, you can construct some bard builds that can dedicate their most valuable spell slots to healing spells. A paladin can act as somewhat of a sub for a cleric too. However, none of them competes with the real thing, not by a long shot. An 18 WIS level 1 healing cleric will heal more than 2x the HP per slot used than any bard, and close to that much more than a paladin.
You also seem to feel that a cleric is good for NOTHING ELSE, yet they have tricks like Bless and Guidance which are really large party boosters. In fact Guidance is almost broken good.
Which is why I say that a party without a cleric is neigh dysfunctional. It will fall below the expected curve. Maybe in the hands of a really superior tactical group with advanced build expertise they'll still be in good shape, but working a cleric into the party will always, always, amplify that.
5e isn't 'cleric dependent' to the degree that AD&D was, where adventuring without one was so hopeless that it was a constant joke in Fineous Fingers, but it is still true that adventuring without one is taking great unnecessary risk, and can easily put success out of reach for many ordinary groups in adventures that would be quite doable with one.