My problem with this is that it creates a break between the mechanic of "prone" and the in-game concept of "prone." I don't want to spend my gaming time thinking up clever translations between crunchspeak and fluffspeak. As far as I'm concerned, "prone" means "flat on the ground." I believe that mechanic should serve concept, not the other way around.
By that logic the bite of a cobra that deals poison damage and a swing from a gargantuan titan's 2-ton greatclub should be identical because they both deal hp damage. Never mind that the first must have inflicted at least a minor puncture in order to inflict the poison and that being directly struck by a 2-ton club would probably liquefy Hercules himself. D&D mechanics are simplifications of fantasy world effects. In the first case the hero probably got bit by the cobra but was tough enough to shrug off the worst effects of the venom. In the second he probably dodged the club and took damage from the nearby impact as it struck the earth like a meteor.
To put it another way, there's no scientific reason why a dagger (1d4) shouldn't be just as deadly as a longsword (1d8). Six inches of good steel can kill you just as dead as two feet of it, and with about the same effort (assuming an unarmed opponent).
I see no reason why prone can't be: guy knocked on his butt, guy knocked on his back, guy knocked on his stomach, guy flipped and propped up in a corner on his neck and shoulders with his legs in the air, snake knocked over after rearing up and needing to writhe for a moment to regain control, or even ooze splattered across the nearby area but rapidly reforming like the liquid terminator. Why would you use six different mechanics to model those when one is sufficient?
A formless cell colony with perfect locomotive and sensory capabilities is fine because it's explicitly a magical creation (or should be).
Killing an ooze using nothing but a pointy stick makes no sense, but making oozes immune to piercing damage renders whole categories of character completely useless (archer rangers, dagger rogues, glaive fighters), so most groups tolerate that break with verisimilitude for the sake of gameplay. That said, with a little DM foresight, one could make it work; just make sure every encounter with an ooze also includes other monsters that are not immune to pointy sticks.
Knocking an ooze prone also makes no sense, and does not have an overriding gameplay reason why it's necessary. Very few characters are so reliant on the trip mechanic as to be rendered useless if it's not allowed. In fact, I think it helps gameplay to have some monsters be resistant or immune to the PCs' favorite tricks; it forces them to change up their tactics.
You're right, there's no overriding gameplay reason why it is necessary. There's also no overriding gameplay reason why it's necessary to deny it, with the added bonus that players usually find it more enjoyable for their powers to work as intended rather than arbitrarily not function (sorry, that's a giant/cat/dragon and I can't envision you tripping it so you can't). You're already "breaking" reality by letting pointy sticks kill the thing (for the sake of fun and convenience) so why not let the guy with the trip power "bend" reality (also for fun)?
I agree that it's good to challenge your players by having some monsters be resistant or immune to the PCs' tricks, I just strongly disagree that the DM should be encouraged to do so arbitrarily. It's one thing to create a (4e) ooze that is immune to tripping or a (4e) undead immune to crits. It's an entirely different thing to grant groups of creatures blanket immunities because you happen to feel like it.
3e and earlier, you got two full-strength black puddings with half the HP. It's still not impossible, but you have to hit each one 5 times in order to kill it, and 31 times in total to defeat a single black pudding. And stupid targeting can leave you fighting up to 16 at once, but hopefully you aren't stupid.
(Of course, if you weren't stupid, you wouldn't be using a pointy stick on it.)
I'm quite aware actually. My party once had to take down an elder black pudding via this method in 3.5. Appallingly, we realized too late that we didn't have a single bludgeoning weapon or damaging spell among the lot of us. In our defense, we had been expecting to fight an unborn god rather than a pudding (the DM chose the stats of an elder black pudding to model the unborn god of fear). Our only saving graces were that most of us had high reflex saves and multiple attacks. We prevailed, but it was a long and very brutal combat.
Again, 3e is my favorite edition, not 4e, but I tend to run games such that there are things you can do, rather than effects you can create - grappling someone is literally grabbing them and holding them, not a catch-all for anything you do that happens to stop someone from moving out of their current square.
I mean, I can't remember the last time anyone's actually fought an ooze in a campaign I ran, because I don't much like them? But if your version of tripping is entangling people with a spiked chain and pulling them off their feet, it's not going to work very well against something with no feet or particular orientation. (I think the last similar thing was a hostile magical machine - a solo trap in 4e terms - that was spewing lasers.)
Also, in practice the well-thought-out justifications tend to be more of a forum thing. Only one of my players - an Exalted refugee

- constantly narrates more than "I up and take a chop at him" in combat, so while the rule of cool would overwhelm minor concerns if they narrated how they were knocking down an ooze and it was vaguely sensible or cool, practically the conversation is going to look more like...
<Player1> roll 1d20+8 Spinning Sweep on the ochre jelly
<Schala> [Roll] Player1 rolls 1d20+8: 11 + 8 = 18. [ Spinning Sweep on the ochre jelly ]
<Imban> << You're sweeping the legs out from under a slime? Really? >>
<Player1> << ...erm, durr. Reaping Strike instead. >>
rather than brilliant narration. Of course, my players would likewise stare at me if I insisted that gorgons were immune to being tripped even though the book says so. I mean, I
still get made fun of for the time a Mutants & Masterminds villain I was running was immune to being grappled for what the players felt was no good reason, and her actual stats sure listed it then. "Oh, right, and is he immune to grapple too?" would probably be the immediate response.
(The funny thing is that we roleplay a lot, it's just that just shooting arrows at a guy rarely gets more than a "twang" and the clatter of virtual dice.)
The OP seems to be planning to run 4e however, which follows a different philosophy than 3.x. Lots of creatures in 3.x have blanket immunities against abilities (undead immune to sneak attack). That doesn't mean that it's necessarily good advice for a 4e DM, which does away with most mass immunities and follows a different design in general.
The well thought out justifications are not just a forum thing, at least for me.
See, in my games it goes more like:
<Player1> Spinning Sweep on the ochre jelly
<Me> << (Assuming I couldn't see a justification for it.) You're knocking the slime prone? How are you doing that? >>
<Player1> << I use my spinning sweep to splatter bits of it all around, so that it has to take a few seconds to put itself back together. >>
<Me> << Fair enough, roll it. >>
If something seems like it shouldn't work I first try to think of a way that it could work, and I ask the player to do the same. It never takes longer than a few moments for someone to come up with something plausible.
In the time I've been running 4e I've said no to a player exactly once, and that was because when I asked him about it he decided it was stupid after all and requested to take a different action (it involved a bloodied troll that would have had to jump into the center of a bonfire due to the Fighter's Come and Get It). If your players are okay with it, fair enough. If everyone is happy it's definitely not badwrongfun.
However, I've had the misfortune of playing under a DM who would arbitrarily deny certain effects that he deemed "unrealistic", even if the player had a justification for why it should work and despite that it upset the player (this DM wouldn't let the player take back his action either). I learned a lot from that guy actually (in the sense of how
not to run a game). The DM is there to act as a fun-inspiring arbiter rather than a my-way-or-the-highway tyrant, and it's a "subtle" difference that many but not all DMs seem to grasp (and no, I'm not suggesting that you are a tyrant DM). Your advice of "striking down nonsense" did strike me as having dangerously tyrannical interpretations though (again, I'm not suggesting that such was your intent).