Sure the JS is a fairly pointless HCP, but the spade shortness is worth something in a trump game.
It's the kind of hand that should definitely be opened, but only at the 1 level. The point of opening the hand is to let partner know you've got something, at which point you're looking for a 4-4 heart fit.
So in my opinion the hand should be opened, a heart response from partner should be supported, and a 'pass' is the probable response to all non-forcing circumstances. The biggest danger I can see in this hand is falling into the "use NT as an exit if nothing else works" trap instead of following the "when there's no fit, quit" rule.
Advertise what you've got, and let partner decide if there's any game here.
Well, that's how I read the hand at least.
Now to carry on to the more general question, could there possibly be a hand that technically should be opened, but in fact really shouldn't be? Sure there is, but it's important to note that it's all dependent on the situation, and not the hand. The main point of opening a "weak opener" is to let your partner know that you've got the points; it follows that the time to NOT open it is when partner doesn't care.
When does partner not care what you've got? When they don't have a hand good enough to do anything about it. When can you know that's the case? When the situation makes it obvious! For example, when you're in 4th seat and LHO and RHO have both bid. LHO obviously has 13+, RHO has 6+, you've got 13, your partner can't have much to talk about; there just aren't enough points in the deck. When the situation tells you something like that, then you know it's time to sit in the weeds and help the opponents dig themselves into a nice deep hole.
In general, yes, you should open a 13 point hand. Because your partner might really want to know. But there will be situations (not hands, situations!) where you shouldn't bid.
Like all good rules in bridge, you have to know when the rule doesn't apply.