World of Warcraft.... Video game RPGs.... Now that Tony Vargas is gone....
Why is it annoying to you that players help each other out in group that has band together to fight deadly monsters, explore trapped dungeons, and solve puzzles TOGETHER... when it actually makes since that they would help each other out as a team for their benefit and the benefit of the group?
I show up to a D&D game, the GM says he needs to move the table, I say "I'll help". He says he needs to clean the table off and setup the map, I say "I'll help". He says he needs to clear a spot on the counter, I say "I'll help". As iserith said, making a downs side to helping your party encourages them to NOT act like a party in a party based game... this seems silly to me. Sure I could pull my back helping my gm move his table but I don't any rule that is designed to convince players to play solo is a good rule. Any deficit to helping is just that. With advantage and requirement for the helping player to have the skill to help they can still role badly and narrate failure of a twitch in your back but mechanically discouraging the attempt seems against the premise of getting together with my friends to adventure both in and out of the game. I want players to help each other when ever possible because that's what people should do in or out of the game when they are working together for a common goal. Standing around watching one person do all the work you could help is jerk thing to do!
I understanding the restrictions on requiring the actual skills to help, room to get in there, lack of tools etc. but it seems to me if you don't want your players to work as a team there is a fundamental flaw to you sitting together to play a group game. If you want your players wanted to play solo they would play a video game. The inability for more than one player to help is a MUCH larger issue than player helping each other "too much". As iserith said,If your just tired or your players saying "I help" then call for fewer tests.
I really feel like this is GM perspective problem not a game design problem. It doesn't slow down the game, it doesn't cause issues with players, and the only people I have ever seen get mad or upset because a player got helped was the GM who wanted players to fail... oddly enough the commonly fail anyway and GM is mad about it on premise not because it actually worked out. Its the same line of arguments I hear about the Guidance spell. People band that spell because it reduces their chance of failure. The only reason that matters is if the GM WANTS players to fail. A GM … in my opinion… should not have a predetermined outcome in mind for tests but should let the chips fall where they may and have success and fail options. If the GM has a REQIREMENT that players fail, then set the test should auto Fail and their is no reason for the GM to call for role and no chance for the players to use the "help action". Don't blame players for working together to try to succeed.
I think it would be reasonable to always assume that any out of combat tasks or skill checks will have the players helping each other where possible. I just think it's up to the DM to decide when the 'help' would give the player advantage and what would happen if they fail.
In your examples of helping the DM at your game, we can imagine how that could be interpereted into skill checks.
Helping the DM clear the table: No skill check needed an no penalties for failure. Helping cuts the clearing time in half.
Helping the DM move the table: If not getting the table moved would mean that you can't play tonight, and if the table may be too heavy to move easily, then it could be a roll. This sounds like a good candidate for making a 'Work Together' check with advantage. Failure could mean that the table still gets moved, but you miss out on valuable play time.
There are other tasks or skill checks that you could help with as well, but how much it helps depends on the circumstances and the ability of the helper. If the sink breaks and the DM is proficient in home repair, he can try to fix it. If you are not proficient, but still want to help, you could go get a bucket and hold a flashlight. That may not be enough to give him advantage, but may speed things up. If you were proficient in home repair and you could both get to the sink at the same time, then it could be a roll with advantage.
If the DM decides that he's going to set the mood by playing some music on his dulcimer, then maybe you can't help with that, but you could pull out your vuvuzela and play along. Perhaps this would give him disadvantage on setting the mood he wanted, or if the group is receptive, it may help (in game terms this would be the DM who decides what rolls are needed and what the effect would be of failure/success).
My main concern is avoiding having every roll made outside of combat automatically being considered as having advantage. The game is not designed for that. I think it's great the players would think of ways to help each other, but I don't want auto advantage on everything. Maybe you can't give another player advantage on his acrobatics roll to cross a rope by saying "I help him", but you could give him advantage if you can shoot a arrow into the far wall with a rope attached to it that he could use to help steady himself. That's the kind of teamwork I am looking for when players want to help each other.