They do not seem to have an evaluation function other than the survey results, and they don't seem to have a heuristic other than "throw random ideas at the things people don't like", that we can see. You're perfectly right that they very well could have a much more involved process we're simply not seeing, but I see no reason to assume this is so. Especially because the only evidence that there *is* more going on behind the scenes is "Well, they're professionals, and professionals aren't incompetent."
Actually, we have two other rather convincing pieces of evidence:

1) It's how they designed every other game they've done until this point.

2) For a company we're so sure is doing this in part because Hasbro doesn't like how the sales of 4e have gone, I really don't see "We're going to design our next flagship product which will carry our line through the next 5 years minimum by throwing random ideas at a dart board, and letting the internet decide on everything!" going over so well in the board meetings.

Yes. We know this because they (or similar people) have designed 3E and 4E, and there are no glaring fundamental design flaws in either of those...

...wait
Aside from what Agent Paper already said, it's also worth pointing out that 3e was such a failure of game design that after WotC dropped it, another company came by, took the exact same game, added some patches and then resold the game to an entire generation of gamers who already owned the game.

Or to put it more succinctly, just because a game has some large flaws does not mean the game is ultimately a bad game. No product is ever perfect, and every abstraction and simulation has holes. The ultimate test of whether or not a game is any good is do the players come back time and time again, even if they have alternatives? I think D&D has proven itself to be a quality game, despite its "glaring flaws."

So, what is the general opinion here about D&D Next?
Personally, I'm cautiously optimistic. There are definitely things they still need to fix, but on the whole I think they're succeeding in creating a system that feels like D&D, is simpler to start and get started in and is generally disconnected enough that you could add or remove parts as you saw fit and still have a workable game. The most recent L&L indicates that they are aware that the current packet is larger than what they have indicated they want the "core" to be, and that the ultimate plan is to pare that down into a core and start moving everything else into packaged modules, and that will certainly be an interesting process to see.

In general, I have noticed a trend, which is that you will most likely find positive opinions of the play test from people who have actually sat down and played with the system, and negative opinions from people who have mostly just read the material. This suggests to me that they need considerable work on their presentation, and that like many things in life, theory is different from practice.

The thing is this: if you believe 3E and 4E are good systems despite their flaws, then I'm not sure why you would want or need a new edition as replacement. If you believe that 3E's and 4E's flaws render them undesirable, then I'm not sure why you believe 5E will be any different. Which brings us to...
Perhaps because you think that if you took the good parts of 3e and the good parts of 4e, and the good parts of 2e and you meshed them together, you'd get an even better system? I think 4e is a good system. It's not my cup of tea, but I play it regularly and I think its good. Same with 3e. Doesn't mean I wouldn't prefer a system that's a better mashup of the best of both.

They still have no clue what they're doing with healing, and it shows. They have several systems in the playtest packet for healing but none of them really seem to work the way they intended.
This is very true, and honestly, I think one thing they ought to consider is just breaking down their system into the core which is the raw, base resolution mechanics and then some "heroic tiers" (as distinct from level tiers in 4e). Say Traditional, High Fantasy and Big Damn Heroes tiers, and at each one just provide the basic mechanics that support that flavor. So traditional might have no or low healing between encounters, slow limited healing per day, fragile characters with random HP progression, pure vancian spells and limited expertise dice. The High Fantasy tier would introduce more available healing, limited at-will spells, a faster expertise dice progression, backgrounds and feats/skills. The Big Damn Heroes tier would introduce more at will and encounter based spell casting, a healing surge mechanic very similar to 4e (with a better indication that at this tier HP is basically a measure of how long you can stay in one individual fight), bigger expertise dice pools with additional powers and maneuvers that don't require expenditure of expertise dice. Then rather than trying to come up with one healing mechanic (and others) to rule them all, they can have individual distinct ones for each play style the tier is trying to encourage.

Anyway, mostly I just want them to pick a single class, say the wizard and actually plan out what it should be doing at what level. Complete it and then develop the rest of the classes around that benchmark. I don't know what they're doing now, but whatever they're trying leaves oddities all over the place that look rushed and poorly thought out.
I think the problem with this is it naturally leads to comparing classes side by side. In some ways I think the best thing for them to do would be to simply design each class independently, asking themselves "If I were playing this class through an adventure and going from level 1 to 10, what would make me have fun?" Then once they have each class that is entertaining on its own merits, they can mash them together and work out the synergies and conflicts. Unfortunately, I think to make that work, they would have to surrender the idea of levels being comparable across classes and all classes leveling and gaining powers at the same time and rate.

As a 4e player, I see a combination of backward steps to legacy mechanics and kind of a craven approach to 4e concepts like minor actions and the "bloodied" condition which are couched in walls of text instead of just being called out. For example, Wizards in the recent playtest had Encounter spells. They weren't called that, but that's what they were. Healing Word? A minor action. Not called that, but that's what it was. It seems clear to me that they're not making the game for me. Mind you - this is fine. I have my games already, and I don't need WotC's blessing.
I think the important thing to realize is that getting into RPGs is a jargon heavy endeavor, and while 4e was great about generally being legal contract clear about what's going on, it was also about as exciting and interesting as reading said legal contracts. For a lot of newer players, this means eyes glazing over, in addition to as they pointed out, people feeling like they had to do something with their full action economy each turn. By simply putting minor actions in where they belong and otherwise leaving them out, and by having an "encounter like" mechanic without having defined "encounters" they're hoping to eliminate some of these problems.