Are Riot Games proving that rule-breakers are encouraged to simply start over
No. They're being told that they are wasting their time (and possibly money) by playing League. At no point does Riot ENCOURAGE* them to try over. The problem is that Riot has no real ability to prevent new accounts, and because they don't actively prevent it (except in a few select fringe cases, i.e. Tyler1), some people interpret that as encouragement.
Riot is saying they aren't welcome, by banning their accounts. Some people don't listen, though. These are the people who think Riot "forces" people to pay for skins multiple times and somehow its a scam on Riot's part.
*I will acknowledge that Riot does tell people that, if they want to continue playing, they'll need to make a new account; they won't be lifting the ban from the previous account. But they don't encourage people to continue playing League, and definitely don't say they SHOULD create new accounts.