Is there an English idiom for when you must commit to a course of action even if it turns out to be the wrong one

Not a literal translation, but a saying that describes a similar situation is:

"The beatings will continue until morale improves."

The expression describes a captain/boss who will be cruel to his subordinates until they improve their efforts, even though the cruelty will probably make the problem worse. (More on the origins of this phrase.)

In (British) English, a painlessly idiomatic usage would be

Mechanic: Do you want to repair your car?

You: Yes, but please don’t go overboard.

As thefreedictionary points out, ‘go overboard’ literally means falling out of a boat, but idiomatically one can also go overboard on a task: ‘to do too much; to be extravagant’.

That can mean a range of things, from taking a task in general more seriously than it could possibly merit, to polishing thousands of tiny details that no-one could possibly ever see.

In the case of your example, the not going overboard scenario would involve the mechanic simply fixing the essential problem efficiently, and stopping there.

John’s colleagues would understand each other perfectly if one of them were simply to say, ‘John is going overboard again.’ They might or might not try to stop him, but they would understand that John is expending unnecessary time and effort, as usual.