No, it is not wide open for hackers - but file integrity checks or generally locking down certain files (which has been confirmed in engine upgrade) would help with some issues largely unrelated to internal/external cheats.
EAC works pretty decently - so does BattlEye if properly updated and configured, which is harder to do compared to EAC due to the company's structure. Long story.
Here's the reality of anti-cheat:
No anti-cheat is perfect. No anti-cheat can be perfect. As long as sensitive memory is stored on the client, that memory can be extracted or manipulated to create cheats. That is just how data works. It is just more or less difficult to attain the rights to touch this memory while remaining undetected - but it is never impossible no matter what you do. Given time and resources entire anti-cheats can be reverse engineered and emulated seeing as they are just software after all.
The only approach you can take to solve this problem is by moving the sensitive memory to the server side. This is why you do not see cheaters in games like Starcraft, League of Legends or Dota. At least meaningful ones. Because of the fog of war mechanic the server will only transmit data that the player should be able to see. The nature of the genre itself prevents cheats from being useful, and and the simplicity of those games makes it easy to move things to the server side, away from the attacker's control.
A good example of this is how cheaters in APB are incapable of manipulating things like car handling or car speed, because the physics simulation for vehicles is handled on the server side. You could technically do the same with player aim and movement and achieve utopia, but sadly the data transmission required would be out of this world and would not work for shooters at all. Our genre simply does not allow for it.
It is an endless battle that can not be won - you can only do your best. I could go into the implementation details that explains why you see such a small quantity of cheaters right now, but somehow I don't think forum moderators would allow me to. For reference,Valve decided to mostly give up in implementing client-side anti-cheat, among other things they do the most basic of scanning based on detected cheats and leave it at that. They moved their efforts onto detecting cheaters based on machine learning using VACNet, there's a good summary of that talk here: https://www.youtube.com/watch?v=SnRgW54EWwA
I've said it before but I'll repeat it again: Right now historically speaking is the lowest amount of cheaters that I have ever witnessed in this game's history. You see occasional appearances but those people are swiftly removed. The other cheaters that people are seeing are a product of paranoia, an incredibly high skill ceiling and bloated egos. People just can not accept that people can be better than themselves.