But for countries with obsessive security operations and deportation targets, the incentive to pass the possible criminal onto the next stage of the process involving different sets of border guards doesn't disappear after you've helped yourself to their petty cash. Indeed if they're not outraged, that's a pretty good indication they're hiding something and you're doing great detective work, and if they are, maybe you just find their comments and threats annoying and want to send them to the deportation centre to know what real mistreatment looks like.
Mine is I've both been robbed, and "not" arrested (but jailed) by border patrol. It doesn't play out how you've claimed. The robberies are swift and then they eject you so they can rob the next guy. The jailings eat up their resources for hours. No one that can rob more innocent people is going to waste their time on a long-shot arrest of the innocent when they could be out there robbing 10x more people. The jailers will actively actually complain to you while you're arrested that it's eating up their time.
Now I'm just some guy on the internet, so I don't expect you to believe my actual reality over the ideological theories you have in your head. So all I have to say is if you keep crossing borders I expect some day you'll learn it the way I've learned it. I didn't come to my conclusions through theory but rather seeing just how much fairer robbery is in real life and how it is better at producing positive incentives.
Or even less your first theory about how a bribe based system is necessary for an immigration system to "bring in good productive people" which frankly is a 180 degree pivot from a story about border guards indiscriminately thieving from everyone, as well as obviously falsified by the many countries where border staff neither demand unofficial payment for entry nor routinely assume that anyone who looks a bit funny is an illegal alien or a drugs mule.
1) US model, guards only rewarded for catching criminals or deporting. Lots of false negatives at no cost to guards so they fuck with you a lot for no apparent reason. Canada somewhat similar.
2) LatAm model, bribes/theft to incentivize the to not burn up time with false negatives, but they sonetimes are rewarded enough for true positives to not just let them go.
3) "Swedish" model. Straight salary and then not give a fuck. Seems everyone gets through with not much thought.
LatAm model seems most practical of what I've seen but I haven't spent much time in Europe or Asia, mostly middle east, the Americas, and southeast asia.
LatAm model where they're too busy robbing people to care about actual threats (who are generally particularly happy to pay them off, including offers of recurring payments) seems like obviously the worst of both worlds. Though frankly my own LatAM border highlights were watching Ecuadorian airport staff meticulously searching the multiple suitcases every local family brought with them from Colombia and then not even bothering with a token gesture at my bag, and having no real issues at land borders despite crossing them with a strikingly different-looking temporary passport. Apparently the Bolivian border guard was enthusiastic enough about his job to give US Americans a lecture on why they had to pay to arrange a visa-on-arrival everyone else got for free
Therefore in the USA corruption model you end up with a bunch of false arrests while in the LatAm corruption model you end up with a bunch of fast robberies but not so much the lengthy deportation/arrest of innocents based on the officer thinking that's the bigger reward.
The way I've had this play out time and time again is my shit gets robbed in the third world but I have no problems entering, and the exact opposite issue with the USA.
Of course you could point to say the Swedish model where as far as I can tell they have no incentive to do any job whatsoever. I've entered Stockholm straight on a flight from a sketchy part of Iraq and no one even bothered to look at me or even question where I was coming from or what I might have with me. Their border guards must just lounge in a room drinking tea and draw their salaries or something.