I agree, and if anything the problem is even worse. You mentioned characters with 6 readings, here's one with more than 30:

https://en.wiktionary.org/wiki/%E7%94%9F

And while you can usually figure out which reading applies based on what follows, there are still many cases where you can't. A standalone 今日 can be any of "konnichi", "kyou" or "konjitsu" depending on context and intent.