Yes, you are right that casinos will never ask you where you get your money from when you visit a gambling place. If you have money, come in. If you have money, come in, if you don't have money, get out. That applies if it's a land-based casino, if it's an online casino, if you have money, please gamble, if you don't have money, please visit the demo mode. Casinos will only serve you when you have some money to bet.
Only if you gamble offline and you are a low bettor
If you try to deposit in online casino from address that is in blacklist for illegal deeds (used for mixing or maybe address was used in scam or exchange hack), you will immediately get account frozen and a request for KYC. As to offline casinos (not sure if it works in every country), if a person is a dirty alimony not payer and tries to make a deposit via bank, casinos will get notified for that. If you bring cash, I think under some limits you can gamble freely, but if you bring a sports bag filled with banknote nominal mix, you will have questions from their security officers 
Still, if that gambler wins big, he or she might need more than an ID to be presented when he withdraws it. Physical casinos won't do that. When you present your ID and at the right age to gamble, you won't be stopped. You win big and want out, you won't be stopped unless you cheat. Some teenagers do have a face that seems like adult enough to be of legal age so they can always pass through establishments that they should not be in. I think both have their cons and pros and some have holes that is being taken advantage of those who wants profit by making ID's or casinos that just wants money but do not care if they are underage or not.