There are downsides in these specific cases, but it's hyperbole to say that it makes open borders "useless". (OP's case wasn't even open borders, it was solved with a good old fashioned war, and would have been fine if he'd left the scan for after the war.)
It does impact auto explore though, because the auto explore does not know about this and will happily drive into occupied space to scan planets for no anomalies.
I'll grant you that there are some minor strategic uses to open borders. However, the fact of the matter is that the current model with regards to anomalies just doesn't even make sense. If you have access to an area of space, you should be able to fully explore what's there.
I mean... Really, the fact that it needs to be explained that you actually CAN'T do that (as it was to the OP) really speaks volumes in this regard. It's simply counter-intuitive and illogically "gamey."
In real life, after all, American scientists can study phenomena in Japanese or European waters, and vice-versa. There's no reason why it shouldn't be the same here.
Hell! It'd even lend credance to those events which pop up every once in a while where the AI closes its borders to the player because they're worried about your scientists "stealing secrets."