This topic is one I've been thinking quite a bit about lately! I'm glad to see it show up here. It's giving me tons of food for thought
1. Tabletop vs MU*
Tabletops are like braiding a rope. There is a limited set of main characters and generally only one person controlling the environment. Unless you have materials that just completely don't work together, you can get something passable in the end without too much effort.
MU*s are like weaving a tapestry. Each person has an individual thread (or two, or three, or five), all of different lengths, and no one can agree on a color scheme or which corner to start from. Without excellent management and defined borders, it's bound to devolve into a mess of rainbow vomit. On the other hand, with that much going into it, you can get some pretty fucking awesome designs, too.
Tabletops are a much more controlled environment from the outset, so you know more or less what you're getting via knowing who you're playing with (or getting to know them via playing). MU*s are always changing and have great capacity for surprise. So with that in mind....
2. Social Dice vs. Physical Dice in a MU*
If a system has a social dice system, my view is PCs should not be exempted from it on the sole account of being PCs. It's better to either take the social dice and throw them out the window completely (which some systems do), or accept the dice as part of the system.
Here's an example of social dice used well as part of a tabletop game:
In a recent episode of Critical Role (a DnD 5e game played over a Twitch stream), a PC had his very rare and valuable flying broom stolen by another PC.
To deal with the theft, both players had to roll, one to steal, the other to detect. Then the thief's player rolled a bluff check to lie about where the broom went, and the victim rolled to detect the bluff. The victim failed both, so the thief got away with the broom scot free.
This is a pretty simple transaction between two players who were friendly (or friendly enough) OOCly. But if you threw the social dice out the window, half of it would be up in the air mechanically, and in a PVP MU* specifically, this interaction might have baited out some OOC drama with some particularly sore losers because the dice would have left an opening for it.
When social dice don't exist:
I have played RPIs that did not make use of social skills. The only social skills built into these types of games were essentially solely used for hiding and eavesdropping, which had all sorts of interesting repercussions. Social interaction was not governed by other skills and entirely left to the wits of the players. In these cases, however, staff NPCs being socially influenced was a rarity; in RPIs, much of the NPC stuff tends to be governed by code to essentially run shops, drop snippets of coded gossip/quest bait, or act as killables. Staff pulling out NPCs that were sentient and could be affected by negotiation of some sort didn't tend to need social code, rules or dice to play them out.
In the cases of these games, everything that had physical effects was solved by dice: combat, sneaking, thievery, assassination, magic (if applicable), and crafting. Everything else was left to RP. Game balance was designed around social interaction being ruled by something other than dice.
Social dice that exist but are not used well:
In many WoD-type MU*s, PVP social dice being nonexistent is often justified by an anti-creep policy. My opinion is this has the side effect of marginalizing social PCs in general. Unless a sphere has a powerful skill branch that makes use of social dice, that category is going to get dumped by a lot of people, because they can't really make use of it in general play. In addition, social resistance merits get dumped even more, because they're essentially worthless when you're hardly ever going to be defending against a social attack. If you're new to WoD MU*s and roll a social character, chances are high you'll never be able to display what your PC was optimized for unless you find the right ST.
Of course, these sort of policies tend to be pretty general, too. Players may roll the aforementioned subterfuge vs. empathy check anyway and staff might not care even if the lie was something completely bald-faced, like, "A unicorn ate your broom." However, they might draw the line at using persuasion to follow the 'unicorn ate your broom' line with 'and you need to give me your wallet so I can try to go buy it back.' Or, they might only draw the line if you then try a persuasion check to use the line, 'And you need to go home with me or else the world will end!!!'
WoD specifically is balanced to have primary, secondary and tertiary fields, but there's an advantage to playing a primarily physical PC in many setups, and to a lesser extent a mental PC, because of the research/crafting component. Socially powerful PCs certainly do exist, but very often it's in tandem with some particularly sweet sphere-specific powers that rely on social dice.
I realize this is not the case in all games. AFAIK, I think Requiem for Kingsmouth(?) had a built-in system for taking advantage of PCs with social skills, which I think is awesome. This is the only example off the top of my head of a game where social dice existed and were used to any effective extent.
3. Non-consent vs. Consent vs. Freeform RP
What's the dividing line between letting something physical be ruled by dice, but not something social? Particularly when physical dice can often have social ramifications? What's the difference between being thrown bodily in a basement and tortured for the location of a macguffin, vs. being bought a few drinks and letting it slip because the charming and pretty person next to you asked nicely?
I understand that many people do draw a line there, but I think it has less to do with the existence of social dice than a consent issue. In the above scenario, without the existence of social dice, a certain type of RPer would say 'I control the emotional impact of this!' and simply not let anything slip because they're too badass to suffer from pain.
4. The Importance of a Well-Defined Ruleset, Setting and Reducing the Sandbox Syndrome
Part of the reason I feel the way I do about social dice is because wiggle room with the rules and mechanics can lead to serious abuse. It's fine if everyone's in it to have fun and everyone accepts the same amount of wiggle room, whether it's for or against their PC, but that's never going to be the case in a large scale game of strangers who play from behind computer screens.
Defining the consent level, setting and ruleset in clear terms reduces confusion. In a tabletop setting the ST would be guiding the process the whole way through. In a MU*, staff simply can't be around 24/7 to simulate the same experience. I believe RPI MUDs tend to compensate by having scripted mobiles and much more emphasis on PVP. MU*s seem to prefer the player ST route, but this can get problematic with player STs not playing true to setting, or otherwise not running arcs that are big enough in scope to be any more than a one-shot.
When players are reduced to a sandbox setting, they tend to get bored and move away. Players have very limited power to change the world, so their storylines tend to stall out without major events to frame them around.
.... that's about as far as I've gotten in working this through my own head. Putting together a MU* is hard. Respect to those who manage to complete them.