I don't think you can kill corporate run gambling - people will just use some offshore website instead. It might be something we should treat more like smoking. - Require a disclosure of the EV of each bet as the user is placing it. E.g.: Expected loss $5. - Ad targeting restrictions.
No they won't, because moving real money to and from these shady offshore websites is a nightmare, and without enforcement there will be too much fraud in the system for the vast majority of regular people to bother.
Gambling is so prevalent today because 1) there is incessant advertising, including being overlaid on the game you are watching and 2) it is convenient, taking like 3 clicks and under a minute to go from scratch to placing bets. You can even use Apple Pay. Take away either of these and participation rates will plummet.
You don't even need to speculate, just look at the numbers. There were countless illegal and gray market gambling options available a decade ago, both online and in-person. How many people were participating back then? I personally didn't know anyone who bet on games outside of maybe the occasional trip to Vegas, and that too was just for the novelty of it. Today >50% of adults in the US are regularly betting online, and the number is growing every year.