Why does an orchestra need administrative staff but a small jazz duet does not?

All of the music is overseen by the music librarian. Smaller ensembles really don't need a librarian for all the parts, if they use music at all. 

An orchestra is a large organization that requires more people to handle it's operations than two persons.

Two people tell their friends and family they'll be playing at the local coffeehouse. Today, they can get the word out on social media. Several dozen people show up.  Maybe the coffeehouse pays them a little something, but most of anything they are paid goes in the tip jar. These two people are not making their living from this, they have other employment to get by.

An orchestra is made up of paid professionals.  Friends, family and social media do not put several hundred to several thousand fannies in high-class auditorium seats on a regular basis. It takes a large organization to advertise, seek outside funding (donations, and the organization is probably a registered non-profit), and otherwise manage a large group of people.

Why did the one-room schoolhouse of 100 and more years ago function with a single teacher and schools of today need all sorts of administration?

Chances are, that major orchestra is registered as a 501c3 non-profit corporation - they are allowed to receive donations, and they have many tax exclusions.  This is a big ship, and it takes a big crew not only on stage, but behind the scenes.

I registered our professional chamber music group (6-8 rotating people per concert) as a NFP in NY.  Royal pain, that paperwork every year.  Eventually let it lapse, and went with just the duo of the 2 of us (flute and piano).  We play a lot of pro bono concerts now, to benefit other arts organizations - we do not need the income, having done well for many decades, and do not need the aggravation anymore, either.  We now can play what we want, where we want, as often or seldom as we want, for whoever we want.  Heaven better have concert venues like these, or I refuse to go.  And 47 years of having my own personal in-house *collaborative pianist* (HOW LUCKY  AM I ???) leads me to now refer to him as my conjugal pianist, or connubial pianist.  It is easier to take care of HIM, than run a NFP.

The Rolling Stones employ a few hundred people. When they go on tour that number probably doubles. Even The Miles Davises of the world have agents and managers and trumpet polishers and drivers.....

The difference is an orchestra has salaried musicians, play enormous venues and have a huge turnover.

Jane and Tina do not.

Is that really difficult for you to understand?