Are you talking about offline gambling? If yes, then if you can check every customers ID before placing a bet (if you can evaluate his age by looking on him), then such casino should stop operating. Its not possible or impossible to check, its a duty to check age. As to online gambling, then yes, its totally impossible to check everyones ID. In fact, rare online casino try to check ID during registration. They usually allow everyone to register freely.
Yes, this is the problem with online casinos in today's era. An underage person could easily fake his identity by talking to a friend and using his credentials to sign up and do the KYC. This can be done especially when that person was offered a payment and in a third world country they will probably accept it even though they don't know the risk they took by lending their own identity.
When it comes to deposits in online casinos, online cash applications are now being accepted and even the underage can make one because it can be used as a savings thing so they are promoting it to be used by kids too.
The filtering system of online casinos is flawed and I doubt it can be fixed that easy because they also want the money, business is business.