I know there are several pages, but I wanted to respond to the OP.
For me personally, I think it does make sense to be able to sneak attack some undead and some golems. Undead and golems both still have moving parts which can be damaged in such a way to hamper them.
I don't believe oozes and jellies have an obviously visible anatomy to target though. I can understand saying they are normally immune to sneak attack.
A good middle ground might be to allow knowledge checks to come into play here. It makes sense to me that a rogue who has studied oozes or undead would be able to pick out the weak points of their anatomy; know where to hit them where it hurts. I like the idea of knowledge skills being made more attractive.
However, that then brings up the question of why a wizard or a fighter who has those knowledge skills couldn't do the same thing. I'm not really sure what the answer to that would be. If I try to think about it too much, I end up realizing that D&D sneak attack doesn't always make sense if I put too much thought into it. Still, I feel like there's some way that what I mentioned here might be used to find a good middle ground between the 3rd Edition way of saying some things are just flatly immune to sneak attack and the 4th/5th edition way of saying everything is just flatly vulnerable to sneak attack.
Out of curiosity, how do things change if we assume a multiclass rogue/fighter split evenly? I'm curious because my current character is a Half-Orc Rogue 1/Fighter 1. I focused on strength and two handed weapons. There are times when it seems as though my damage is quite high.
However, the character in the group who currently seems to somewhat break the game is a barbarian who has focused on two weapon fighting. He gets to add his bonus rage damage to each attack; even with something like a whip or a dagger in his off-hand, there are times when it seems over-the-top compared to other characters.
You seem to have a better grasp of the end game than I do, so I propose the question to you concerning how these options play out at higher levels. I'm mainly familiar with levels 1-4 of 5th Edition.
(Replying to the question, although I think pure DPS isn't really anything to do with this thread much)
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Taking an even mixture of the two notional characters in the example I worked out, you can go either strength-based or dexterity based.
For the strength-based Fighter/Rogue, using a greatsword as in the fighter example, you end up doing 20.55 damage per round average, with sneak attacks doing an extra 3d6 15 rounds out of 16, for a total average damage (factoring in sneak and misses) of 30.39 damage at level 20. Once per fight you can also take an extra attack action which will do a further 20.55 damage on average. So, a tiny bit worse than a pure (DEX based, with an additional feat) rogue on average, but the extra action makes a difference when you need it.
Going the DEX based approach I ended up speccing out a rapier and handaxe build (handaxes being light *and* throwable, which is useful for a dex-fighter). Assuming two weapon fighting, the duel-wielder feat and at least one of the fighting styles chosen to be two weapon fighting, you end up with three attacks per round (two rapier, one handaxe) and using your sneak attack damage 63 in 64 rounds (remember, this is still against the pit fiend, AC 17). That comes out to 21.825 damage on average for a round, or 32.16 factoring in sneaks, misses etc. However, the "extra" comes from this build having an extra feat compared to the strength-based fighter. The fighter and rogue I chose was a very lightly optimised rogue and a very basic fighter, to prove that the fighter didn't need any advantage to outdamage the rogue. Combining them in the most obvious ways leads to a very basic strength-based fighter/rogue and a slightly optimised dex-based one.
It's also worth noting that by "optimised" here, I mean only "character options spent on improving combat ability". Each of these characters would have six ability score increases (or feats), and assuming the primary combat stat started out at 14 (very conservative; I'd be unsurprised if it started at 16 for most characters that were primarily combat-oriented) no more than three or four have been spent. Either two or three ability score increases or feats are unspecified, and would probably have gone into optimising something other than pure combat.
As to the barbarian... Going with the traditional greataxe, and taking a pure barbarian to level 20... and assuming that the character can rage every turn of a combat (so we're looking at a "highest possible average" here. the math is a bit more complex since there's advantage and one attack if the barbarian misses, but here's some rough figures for attacking an AC 17 creature:
At level 20 there are two attacks per round, dealing avg 15.5 per normal hit and average 34 per crit. Crits are 1 in 10, normal hits 15 in 16 (both due to advantage) which means each attack does 17.93 damage for a total of 35.8625 damage.
One round in eight at least one of the attacks miss, and the barbarian gets an extra attack, again doing 17.93 - which brings the total average damage per round to 38.1.
Going for a TWF build instead... the best you can do is 1d8 for the main hand and 1d6 for the off hand (1d8 is the best you can do, one handed)
Main hand damage: 1d8 + 5 + 4 = 13.5 average, 8 + 4 + 5 + 2d8 = 26 average for a crit. Average per round: 15.26
Off hand (No damage bonus from STR): 1d6 + 4 = 7.5 avg, 6 + 4 + 2d6 = 17 average for a crit. Average per round: 8.73
Which comes out at 39.24 per round, plus the extra attack on rounds with a miss... a total damage output of 42.10
... You know, I expected to find the barbarian overpowered here - it certainly has felt it at the table. However, in at least this test, it's just right. Barbarians will do more damage *in one round* than a fighter could, but the fighter not only makes up for it on average (total average damage output of 41.1 for the fighter, or exactly 1.0 points less than the barbarian) but the fighter can *also* choose to attack twice, increasing damage to 82.2 twice per combat. Which means the fighter is basically as good, but is able to tactically choose when to completely swing things their way. And the fighter is attacking four or eight times in a round, so they could utterly decimate hordes of weaker creatures.
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Hell, this is too long. Putting the whole thing in a spoiler block so as not to bore people who aren't interested.
TLDR: Fighter/Rogues are (in terms of pure combat, against AC 17) better than pure rogues and not as good as pure fighters. A feat adds something like +1.77 to average damage. Barbarians to my surprise aren't actually overpowered, they're just a lot swingier than Fighters. A level 20 fighter with no feats can outperform a barbarian with one feat, all else being roughly equal... so long as the fight doesn't last for more than 82 rounds. All the above is on average, and please remember that damage per round averages are only one facet. And not really related to this thread, except as background information.
This is also the issue highlighted in the article that started this discussion. You may view SA different than others - but I am not debating just your view of it.
