Yes it is. It’s not some unobtainable solution like you need to give 1/10 of your pay or giving away your freedom. It’s easy, free and almost painless solution that will solve your problems. You can’t try to cure your lung cancer and continue smoking.
If thats the point where you want to draw the line, I guess that it becomes dumb at exactly that point.
But the point of the thought experiment is that it says what you said: it will definitelly happen because infinity is absurdly big number.