If the government want to fight this, they first need to banned physical gambling place around school area. You find it difficult to see tertiary institutions that doesn't have a gambling place where student comes and waste their money unless it's far from town. School public wifi also need to banned some casino website, this way they wouldn't be able to access some popular casino online. This might not be the best solution but it will do some control to student gambling addiction.
Maybe this your suggestion will work to an extent but to a large extent, it won't work because students can still gamble online. Gambling has come to stay whether you like it or not because since the coming of the online gambling and casinos, gambling has gotten a wider coverage and can’t be controlled because even when the countries governments try to control it, people will still use VPNs to have access to the gambling sites.
Sad reality, the best thing is to utilize every resources that the government have to prevent those young students to get involve into gambling, proper awareness and school guidance and more specific information about what might be the bad effects of gambling, as you mentioned, it's very difficult to stop this as even the government have that capabilities to ban it with their jurisdictions gamblers can still find ways by every means that the interntt can offer.