Couldn’t this just...still be happening? Wouldn’t this general average concept only provide better cover for a secret bribing system?

Indeed you can still bribe the captain for throwing someone else's cargo out, but that wouldn't bring you any benefits, except of some hassle. In the event of cargo being thrown out, you will have to pay your part of the loss, regardless of if it was your crate that was thrown out or someone else's. If it was your crate, you will get its value replaced (minus your part of the lost value ofc). As there is no damage, why would you want to bribe them?

Declare your cargo as hardly worth anything, then actually send gold bars, and bribe the captain...

Then the port mysteriously loses your cargo, and compensates you the full $500 you said it was worth.

Declare your cargo as being gold, then actually send lead bars, and bribe the captain to dump it.

I mean if I have important or. valuable cargo, let’s say MacBook Pros, it seems efficient and beneficial to have some clothes thrown out first before my container.

Not if they spend so long moving aside your laptops to find the clothing that the entire ship sinks. With General Average they can sort out the problem ASAP and then do the math later to repay you so that you and the clothing manufacturer both only lose 10% of your cargo’s respective values.

If three people died trying to save your MacBook Pro, that'd be bad. Which is why the idea is based around not caring what's in a given container.