Gambling site is not a bank, nor it is an exchange. Most gamblers, more than 90% of them, deposit on a gambling platform only what they can afford to lose. They are not like "The more money I invest in it, the more profit I will get." Only sick people think that way, only so called "problem gamblers" see gambling as some sort of a business, and, fortunately, there's less than 10% of them among gamblers. So, can it be mandatory for gambling sites to show proof of money to those people, to problem gamblers? I don't think so. Those people need professional medical treatment rather than "proof of money", something that will likely only worsen their condition.
That is true for some but I think there are some who bets more than what they can afford because this is gambling man and it is addicting or someone will get annoyed when they lose so they will try to deposit again in the hopes of recovery. Also there are gambling sites that can work like a bank or an exchange where they allow gamblers to invest money on them.
If you are a gambler whose aim is to make profit, you believe that the more capital you have the more your chances of winning because you can be able to spin more and there are cases where big multipliers came out the longer you play the game. This is why showing proof of money is necessary.
This is a horrible approach to gambling, and I would advise strongly against it. Although it is true that the higher your bets, the more you can win, we shouldn't forget that we are always a bit more likely to lose. That is why we should never risk more than we can afford to lose, no matter how big our imaginary potential rewards can be.
As for the "showing proof of money", I think only governmental regulators can say if that "proof" is really a proof. Regular folks like us can be easily fooled.