Sports gambling ads have ruined sports media. State lottery ads are even worse. The government should not spend money to encourage its own citizens to partake in harmful activities.
If there are no ads to tell you, you have to, first, be informed that sports gambling is a thing people do, then decide that it's a thing you want participate in, and then obtain information on how it's done. This adds friction. Friction reduces participation. But if you really want to gamble? You still can.
Is it advertising when the announcer for a game talks about gambling? There's statements that obviously would be advertising, so the interesting thing is where and how to draw the line.
If an announcer just wants to talk about gambling, fine, I guess, but I really doubt that there are any announcers that would do much of that.
That should push the shadier operators out of the limelight, though it would likely leave large-pot gaming (sports, Powerball, etc.) standing, at least for a while.
(I'd very much like to hear criticisms of this approach.)