I think that someone who is confirmed to be on a fresh account only to continue breaking the rules should immediately subject their main account to the next punishment. Or an immediate perma-ban if their main was already perma-ban.
Unfortunately, I think Riot should be realistic here. It can't be something that is done for every single ban. Most punishments are done automatically.
The amount of effort that would go into watching the IP address of someone that was banned while questions such as, "Is this them, or someone else? Did the person we ban have a dynamic IP? Is this a dorm that they're playing from? Etc." always have to be asked to avoid banning someone falsely make the whole endeavor not worth it in most cases. Imagine spending even 10 hours of time and money (collectively) only to decide, "eh, might not be the person. Better not ban to be safe".
When the rare moment comes around and they ban multiple accounts for somebody all at once I doubt they are basing it just by IP address. They are likely basing it off of a slew of information such as behavioral habits in chat, gameplay habits, APM, etc. Not a small amount of effort and not something they can assign automatically.
And let's face it. If someone hops on a new account and doesn't break the rules there is no reason to not allow them to continue playing. It's not like they're bypassing the punishment if they do so after a perma-ban. They lost all their progress and content on that account. That is no small thing.