Enemy ships probably shouldn't be able to walk up to your front door unnoticed.

Terrible idea.The sensors and stealth game is a massive part of the fun in 4x games.In fact GC3 should be more sophisticated in that manner.

Not if you take precaution.

How about deploying Listening Posts/Spy outposts along your borders?You don't magically see what's inside your own borders. If you can't bother defending your way home, the game shouldn't do it for you.

Crippling your eyes should be an invader's or intruder's first order of business.

That would make sensors mostly useless in my opinion.  So, I will have to disagree, considering people would just go for influence boosting tech, rather than sensor tech.

I don't know about you, but I have the map mostly explored before I hit the second sensor tech.  I use sensors to watch over my territory and keep a constant eye on opponents.  I also see no reason for influence to magically grant awareness.

edit: Especially considering I can stack enough influence on one planet to cover 1/4 of a gigantic sized map with influence.

That's why sensor tech is important, both on ships and Space stations. This is a part of strategy.

Edit: Noticed now others had answered him with sense already.