I am nearly finished giving my first ever watercolour course over eight weeks. I included some colour theory for my students based around using six primaries - 3 of each primary in both a cool and warm.
Having the knowledge to mix a bright secondary means you can always have a good colour on hand and not have to reach for a ready made tube colour. Its all about understanding your pigments and their bias so when you work with a limited set of colours you can really get to understand their properties.
You can always dull down a bright colour but in watercolour it is not very easy to brighten up a dull colour as this is where mud will happen.
For a bright orange it is important to use a Warm yellow and a Warm Red. This avoids them having any blue bias so the secondary will mix bright.
Here I compare using a very popular tube orange Schmincke Translucent Orange versus mixing two primaries this time Winsor Yellow and Scarlet Lake. The tube sample is more intense but I think with the mixed wet into wet I only needed to have a stronger mix of pigment. The lovely result (sample top right) comes from just dropping the colours in and leaving them which results in lovely varying shades of orange, bright and clean.