It really depends what someone is playing. Most "Tanks" and "Juggernauts" you can actually play on high (150-200) ping fairly safely. Other champions, not so much. Ones like Riven, Jayce, Nidalee, etc. require REALLY low ping because they have internal cool timers that are drastically affected by high ping.
The real issue is a lot of people have things like Mobile Hotspots, Satellite, and the good ole' neighbors WiFi, which are unpredictable. Maybe normally the connection is solid and doesn't have problems.. then sporadically in the middle of a game it begins acting up for whatever reason. If you use a Mobile Hotspot, anything can cause issues from network congestion (high increase of users using their phones) to bad weather conditions (storms interfering with the connection).
Then you also have things like Steam and Windows Update, which can strike even a good connection dead at any time. I can't even begin to describe how much I hate Windows Update. On Windows 10 Home, there isn't even an option to make it manually install... so anyone with that OS (i.e. ME) is at Microsoft's beckoning. Steam obviously can be controlled, but a lot of people leave it open and it can cause some serious lag unless you have both a really good processor and internet connection.
There's way too many factors that can affect a connection that Riot Games literally can't do anything about people with high ping. Not everyone has high ping for the same reasons, and not everyone is affected the same way because some champions can be played just fine on higher ping.