That's the ideal. Except that in the status quo, only the good teachers need to get the kids that don't want to DO anything to DO anything, and the practical consequences for failing to motivate the slackers are nil.
Otherwise, there are two basic possibilities depending on the kid's parents. Either the kid is expected to try and DO something (and does), or the parent only expects child care. In the latter case, avoiding willful destruction and interruption is all that is required … tada, babysitting!
The manager analogy doesn't make sense because managers are much more directly accountable for whether the employees achieve anything for the company while clocking in. If managers' mostly subjective assessments were the only tangible output of employee time and other impacts were felt years later and weren't directly ascribable to an individual manager, then maybe the analogy would work.
Babysitters don't have to get the kids to DO anything.
Saying these are the same is like saying a manager in a business is only supposed to check if employees showed up and clocked in.
Sure, some managers are that bad at their job, but it is also very clear that their job is supposed to be much more than that.
Same with teachers. Getting 30 children who did not choose to be there to actually DO something is a very different skillset than babysitting.
/rant