Open Borders is far from useless, actually.  First off, it give a nice boost to your diplomatic standing with the other party.  Much more importantly, it takes AWAY the diplomatic penalty for having ships or starbases in the other person's sphere of influence.  

These are not small things if one cares about diplomacy in the slightest.  And one really should care, if only for UP votes.

Secondly, it can be sold for a small of amount of recurring cash (every 50 turns or so).  The more people in the game, the more this stacks up.

Now, sure, if all one cares about is getting one's murder on, as Adam from Stardock puts it, then perhaps one doesn't care about Open Borders.  On the other hand, being able to put starbases in other people's sphere of influence without the AI getting pissed off is a tremendous advantage.

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As for this being an oversight, it's just the opposite.  THIS IS INTENTIONAL.  Why?  Because those are NOT your political borders.  They are simply indicative of your cultural influence.

Now the reason why the AI gets bitchy about ships/starbases in it's SoI, is because.... it is mimicking how human players feel about it.

Now one can criticize the design all one wants. Lots of people have.  But it is absolutely intentional and central to a good chunk of the game design.  From things as simple as how the AI views things to more complex things like how UP resolutions to turn them into political borders might affect the game.

And a very clever and insightful intention it is, indeed. It truly makes the game better as a game in that you need to plan ahead. If you don't want the AI ships to be where they are then what's the problem? Just shoot the offending ships to bits and be done with it. If you park enough of your ships near the AI's system it will also declare war and try to shoot yours, so duh.

In any case Space is big. Very big. Borders in space are an exercise in futility if not outright silly. Instead, it's about control of resources and denial of expansion. You plant down colonies and starbases to control planetary production and mined goodies and gather enough force to keep them in your control and position them so as to keep the competition away.

Is the AI looking like it's trying to snatch a planet or resource that you have earmarked as "yours"? If not, or you know you will grab it first, then why should you care? What can the AI do with empty space? If OTOH you think the AI is going for the price and probably going to get there before you can manage to get a colony ship or constructor there fast enough, then shoot the damn thing. Surely you positioned a force near a "claim" to make that claim stick.

Besides, you can always make peace afterwards. It's not like there's an Interstellar Criminal Court or something charging you for blowing up 2.5 billion civilian colonists...

The current system seems to be well thought out:

1. Civilan ships NEED to be able to pass at any time in order to enable setting up of trading routes, colonize a planet in another players influence (which is not an actual border - like mentioned above), and snatch resources from other players without entering war automatically. If there is an auto-war response in such cases the cultural war aspect is lost as well as the trading mechanic needs to be redesigned

2. Influence "border" still has a strong effect though as it gives a diplomacy penalty if you cross it, takes away planets from other players without war (which is awesome and adds additional advantages and disadvantages to tactical combat depending on ideology perks (like reducing hit points of enemy vessels or giving an escort fighter to all of your ships)

3. The Open Border treaty negates the diplomacy penalty of cultural transgression (planets, bases on their territory)as well as enabling the player to move any military fleet  across to another target which is a major plus when warring with other nations who do not have this treaty with them and if they send ships to combat you they risk pissing them off

It's funny that the A.I will pay you for it even though it's not relevant to them.

I'd prefer to avoid closed borders too tbh. There just needs to be a few caveats:

1) Ships should always choose to avoid space which you don't have an open borders treaty to enter unless it's impossible to get to it's destination otherwise, or it's specifically ordered into it.

2) The AI should react much more aggressively to unauthorized entry of its space. As in, move ships to shadow and declare war after 2-3 turns of continuous violations.

1) simply avoids having to micro so much, since my auto-explorers currently completely ignore influence borders and constantly cause friction. 2) will force the player to actually respect borders until he's powerful enough to get away with it.