Sorry for the delay in getting back to y'all, but ...
Out of curiosity, what system(s) do you consider to have "in-built mechanical support", and to what degree? (I expect 4E is one, but somehow I doubt its the only one)
4E certainly is one, but really D&D 3.0 and onwards has worked towards incorporating these sort of things - and Pathfinder, in particular, has done a good job of taking away the nigh-auto-fail nature of the untrained maneuver attempt that 3.0 and 3.5 had, as well as expanding on the available options.
I don't want to derail this into a rule discussion but really, how would you do that in 3e/4e beyond DM fiat?
I admit that I may have rather stepped in it with my specific example. I can't think of a single ruleset that actually has explicit table-throwing rules.

(Although I wouldn't put it past Rolemaster to have a table table, cross-referenced by type of wood and square-footage ...*)
As you point out, in the specific instance, I'm probably trying to do something like knock the badguys down. Or, maybe, I'm trying to push them back. Mayhaps, though, I want to pin them under the table.
While it
will take a decent DM to adjudicate this perfectly, I believe that the fact that the ruleset already includes rules for adjudicating tripping, forced movement (like Bull Rush or Reposition), grappling, and / or being caught under large objects means that it is more likely that a new DM will adjudicate it at least competently, fairly, and consistently.
In my opinion, the more rules artifacts a DM has as touchstones when deciding how something new will work, the more likely a fair and consistent ruling is to come out of it. As with Fermi estimates and business planning, it's better to make a series of small guesses than one large one. It's better to treat this as an area-effect trip attempt with a ranged touch attack by the table-tosser to start it off than it is to pick a single pass-or-fail DC.
* Rolemaster: There's a Chart for That! And I kid only because I love - and because the guys I played RM with always had all the charts preprinted in separate, character-specific binders, and it worked fantastically.