If sleep cycles last for multiples of 90 minutes, why is it recommended that we sleep for an average of 8 hours each night?

It's approximate.

Something I know the answer to!

Robert Owen started ushing for the 10 hour work day in 1810 in England. Mind, this is right in the Industrial Revolution where people (men, women, and children) were working for 16 hours a day, 6 days a week, and for shit pay.

So he was pushing for a ten hour work day, but his ultimate goal was the 8 hour day; or as his slogan goes: "Eight hours' labour, Eight hours' recreation, Eight hours' rest".

It was completely arbitrary and just meant to be a compromise between the laborers and the businesses... yet here we still are. Arbitrarily working 8 hours a day. Even though my contract is fixed price and I completed all of my work by 10:00 AM. Nevermind, I'll just contribute to the traffic problem and waste my life away at my desk.

But that's a separate issue. As for whether it's scientifically proven that humans need 8 hours or horrible things will happen, I've had trouble finding. A simple google search only finds news articles and stupid health and welness sights, neither of which site their sources, merely contribute this idea as a well-known fact.

When searching on the first sleep science journal I found, I got some different results:

Sleeping too long (9-10 hours) not too short (5-6 hours) makes you more susceptible to cancer (by like 1%)

According to their parents, 17-18 year olds drive better if they have 8 hours of sleep rather than 7, but of this study they are the only ones to think so (it was all self reported)

This one seemed the most revealing:

Adolescents and Anxiety

If teenagers get less sleep, they are more likely to have anxiety or suicidal ideation. Of course the correlation could also be stated as such: teenagers are likely to get less sleep if they have anxiety or suicidal ideation. They're also just as likely to get less sleep for being old, having peer related issues, or simply being a girl. The causation, to me, doesn't seem clear.

Sleep duration pattern and chronic diseases in Brazilian adults (ISACAMP, 2008/09)

"The sleep pattern of nine or more hours was more prevalent among those with less than 40 years of age, among those who were divorced, or single, among those with a lower level of schooling, those who did not work and housewives. Both short and long sleep patterns were more prevalent among individuals with heart disease, vascular problems, rheumatism/arthritis/arthrosis, osteoporosis, or emotional problems." So it sounds pretty clear to me that all types of people sleep all types of ways. It also says "The prevalence of the short sleep duration was greater among individuals with back problems and those with three or more health conditions." and "The prevalence of six or fewer hours of sleep was greater among individuals aged 40 years or older and among divorced or single individuals." And I'm left wondering about causation again. Did they start sleeping poorly because they have a bad back or did they get a bad back because they sleep poorly? Are they sleeping poorly because they're lonely or are they lonely because they're not getting sleep.

So in my very short and not remotely in depth search, I really havent found overwhelming research saying "If you do not get 8 hours, you WILL get heart disease and you WILL die."

I can't stand 8 hours. I'm fresh at 6. I'm fresh at 12. I struggle in between.

It's so you're in bed for the 20-30 minutes most people need to fall asleep. If you need an hour to fall asleep, you should allot yourself 8.5 hrs or so