How important is it to move the printer's controller board outside of an enclosure?
It depends on what kinds of prints you make, and especially what kind of materials you want to use.
Certain materials (ABS especially, but also PETG to some degree) will print much better if the entire build area, which usually includes the printer chassis and controls, is enclosed to protect from drafts and allow a much higher ambient temperature.
If you print often with these materials, and the control board is included in that enclosed area, you will significantly reduce the life of the electronic components, especially the capacitors on the board1.
On the other hand, if you print mainly with PLA, which is not as susceptible to issues requiring an enclosure, and prints better with an ambient temperature closer to room temperature, you can put the electronic controls wherever you want.

1 See especially this excerpt from the section on &quot;Premature Failure&quot;:

Electrolytic capacitors that operate at a lower temperature can have a considerably longer lifespan.