When I talk with parents abut the dangers of unwanted help, they will often ask how to tell the difference between being responsive and being intrustive. I usually suggest that they let their children them the difference. Since the children won't do it with words, probably, this means being alert to their signals. The most difficult challenge is not to have hurt feelings when they send a "leave me alone, let me do it" signal. If children send such a signal, parents needn't apologize or make a big thing of it; they can just say, "Sure," and go on about their business.
. . . If parents look hurt of disappointed when their suggestions are not eagerly welcomed, after a while the child will begin to think, "When Dad or Mom suggests something, I'd better do it, or otherwise they'll feel bad." Using these feelings, or the fear of these feelings, to get children to do what we want is much worse than giving plain old-fashioned commands. if parents themselves can't stop from being hurt when their suggestions are turned down, it is better for them to stop making them.
Even if children do go along with suggestions for games, it's better not to make too many of them. If we're always thinking up neat things for the kids to do, they won't have enough time to think up things of their own. Beyond that, they may get the idea that all good ideas come from adults, and so become dependent on us. It's nice to entertain children some of the time, but it wouldn't make any sense to get ourselves out of the full-time teaching business only to put ourselves into the full-time entertainment business. We have things of our own to do. So, even with good ideas, moderation is important.