<p>PLA is flammable, but a good case can protect the main board from dirt.</p>
<p>Is it worthwhile to protect a circuit board with a 3d printed case?</p>

It depends.
Protecting your electronics from being touched by random bits of conductive material which would short and fry them is always a good idea.
If it's something that will be visible, then a pleasant printed casing might go well. You might just as well use any other casing though, there's no requirement it be 3D printed.
For a very small circuitboard (an inch or less) heatshrink tubing might be a better form of protection. Or just insulating tape.
If you never intend to access the circuitry again and heat dissipation isn't a big issue, then just putting the whole lot in potting compound may work best for you - complete waterproofing and environmental protection.
Or you could just tape a bit of plastic from a 2l coke bottle over it, and get 99% of the protection you'll ever need, and still keep the circuit visible and accessible.
Ultimately, it boils down to: Do you want it to be covered? If so, by what? If you would prefer a 3D printed case, then do you want it enough that it is worth the time and effort to you?