My players new to RPGs struggle with a game that is as wide open as RPGs. "What can I do?" is a common question and responses like "Well, what do you want to do?" sometimes frustrate them. It takes them a while to grasps the possibilities allowed by the game, so some specific rules (player cheat sheet) to master really helps them form their understanding of how to play the game.
I generally agree with your post, but from a game design standpoint there is a really fine line to walk here.
In 1e AD&D it was my experience that no one proposed to trip, push, tackle, grapple, throw, kick, disarm or sunder anything. Why? Because the rules did not provide for such actions, and the situations where such actions might be warranted came up so rarely that by the time they did come up the player had been trained into a routine which did not include any of those things. It wasn't merely the that player knew the rules didn't provide for such options and so didn't propose them, it's that the player could not imagine those options. They were outside of the players mental framework. To make matters worse, the DM was poorly equipped with tools to handle those sorts of options, and - if he was a wise DM - very much realized the rules he was provided with to handle them were no good, and as such did not want to steer the players into those options even if he could imagine them.
However, while that was true, the very lack of rules overall and the opacity of the rules to the player meant that outside of the combat sequence, the player wasn't hidebound and was very open to creative problem solving, prodding the environment, and interacting with the environment. On the other hand, the DM was poorly equipped to handle those actions and had to resort to ad hoc rulings, and as a result lots of table arguments arose regarding what the right way to handle the situation actually was.
Fast forward to 3e, and we see that the solutions that 3e tried to provide could also be weaknesses. Combat had lots of explicit options called out to the players in the PH, and players had recourse to them and could purpose to push zombies off cliffs or ghouls away from stricken comrades, or grapple wizards, or whatever came to mind. And likewise, there was a rich set of rules available for DMs to adjudicate whatever proposition the players gave. But conversely, the very richness of the rules tended to give the impression to both players and DMs that the only valid propositions where the ones outlined in the rules. In other words, players and DMs came to believe that anything not explicitly permitted by the rules was forbidden, rather than assuming that anything that was not explicitly forbidden was permitted.
When you are feeding players rules, you need to be careful to open up opportunities and not close them off. You want to say, "These are some common actions you might propose, but they are by no means all the actions you might propose."