There are several issues here.
The first is the obvious Strength per Diameter issue and tippets win over line both for fluorocarbon and nylon mono.
This is not just a theoretical advantage in fluorocarbon that is used mainly underwater. A thinner tippet has less surface area that is proportional to the square of the diameter. So not only will a thinner tippet sink faster but it will have less drag through the water to pull on the fly. So visibility is not the only issue. Thinner tippets reduce drag.
The second, less obvious reason to buy the tippet, is suppleness. In most instances tippet should be supple because they are on the end of leaders and suppleness is the ability that allows flies to move more freely. A stiff tippet of the same diameter as a supple tippet will tend to straighten rather than to fall with slack. Slack allows a drag free drift.
Not all fluorocarbon tippets are the same. Seaguar Grand Max is the most supple fluorocarbon that is commonly available in the USA and has good breaking strength.