Even if you try to reduce the amount you allow them to have access to for their upkeep, if they still want to spare some that could be used for gambling, they can still do that as long as they have time to go out and mingle with friends. Everything can be made possible.
The law in your country is really strong for them to hold down people below 18 years old from gambling; here in my country it's hard for you to even see someone go into a gambling shop with an ID card; they don't take that seriously here unless when necessary.
If what you are doing to keep them under control is working, then you don't have to worry about being seen as someone who is overcontrolling them. What matters is that you have been able to save them from the danger of social media, but then again, do you know that they can still be making use of social media in school with their middle school mate gadget, as they don't necessarily need to only use their own personal phone before they can get it?
One thing that makes parenting work easy most times is if the child is an obedient one and is ready to adhere to what the parent is saying; if not, this generational kid is smarter than what we can imagine.