Sorry, I guess I read in 'without DM intervention' and 'at the same time.'
That's actually the key. I play with a group of older people and we have known each other for years, for example people know to roll their own concentration checks to maintain a spell and will just tell the DM if they fail with no supervision whatsoever. For us its all "the spirit of the thing." All of us started play at least with the 2e, so we just "get it" as it were.
The whole idea is that the DM is not "against" the players, he is merely the umpire and narrator. When I see AL or groups in stores too many do not realize this is the case, and it isn't explained to them.
There are tools all over the rulebooks to slow down the powergamers, but the rules are everywhere as opposed to a specific section. For example there was a debate here I was in from a powergamer that his level 14 Brb/Fighter GWM Polearm specialist "locked down" Tiamat is the Dragons adventure. I asked how was that possible considering "Tiamat has greater reach on all physical attacks, breathe weapons, and flying, was you DM not using those?" To me that's a DM fail. When I ran it with a 4 person group I had to reason Tiamat is so massive that she couldn't attack the same character with more than 2 attacks due to lack of "room."
I think Wizards sort of feels the same way, in Storm Kings Thunder they send a few Storm Giants to help out
As far as play though, you have to get a feel for your group. The hardest to DM are the power gamers, since they also believe that the DM isn't the final word, the rules are, and any anything against the way they read the ruleset is you screwing them. They are LE in essence.
Most kids are power gamers but easy to deal with, they are motivated to be great heroes and not "beat the DM." They just see Legolas kill everything and not take a point of damage and think they can do that at first level. Its not in any way mean spirited or intentional. I had to explain to my kids that you cant shoot 3 arrows at once at the start and the monsters get attacks too and are not all terrible at it.
Veteran gamers are generally the easiest, they get that its a story and just say sure, some relish being put in crazy situations. I would suggest everyone who wants to DM get a copy of the old adventure A4, In the Dungeons of the Slave Lords. The characters start out in a dungeon with no equipment or spells under a volcanic island, which of course starts to erupt and shake the island to motivate the characters to move. I thought it was great the first time I played it, and still think its a great idea to really see what your players got. This would work even better today with cantrips and spell recovery.
In the A1 module, Slave Pits of the Undercity, you can see how small monsters can be a great challenge if played to their intelligence. For example, orcs with a bellows used as a flamethrower? Sign me up!
The most dangerous are the ones that are intelligent with no need to sleep, they have %50 more time on their hands then the characters to work around the clock, so don't be afraid to use intricate plans and traps.
As a DM don't be afraid of the power gamers, you can always power game them right back, using every rule in the book.