calendar – Color keys for large data sets?

I have a task to create a day-by-day calendar list within a SaaS platform.

The calendar will encompass many different types of events and roles within the software. As part of this calendar, the Client feels it is important to show a color key for each type of event to clear up user confusion when quickly browsing events. For reference, a common use case would be that a user has 450+ events happening on a single day. There will be a total of 6 event types amongst the hundreds a user will see daily.

I’ve done a lot of digging for UI inspiration, and noticed something- most software does not include a color key in big or small event lists. I cannot find any particular reason that most mainstream software does NOT use a color key in their calendars. Perhaps this is because the data is not quite as large with what I am working with. Is there any reason people more seasoned than myself think that I should or shouldn’t include a color key when defining event types?