When you have a setup that allows you to switch between triode and pentode, you should understand that the amplifier is likely optimized for pentode rather than triode.
Triodes have a lower output impedance and so will need a lower turns ratio on the output transformer. Its really unlikely that is being dealt with properly in most switchable designs.
To answer the question though, triodes are the most linear form of amplification. Pentodes are not so linear, and usually require feedback to keep distortion to a reasonable level. Feedback is not perfect and always causes the amplifier to sound brighter even though it may not affect bandwidth. So a lot of triode amplifier designers don't use it because they can get smoother sound.
So there is a lot more here than just operating a pentode in triode mode!
Triodes have a lower output impedance and so will need a lower turns ratio on the output transformer. Its really unlikely that is being dealt with properly in most switchable designs.
To answer the question though, triodes are the most linear form of amplification. Pentodes are not so linear, and usually require feedback to keep distortion to a reasonable level. Feedback is not perfect and always causes the amplifier to sound brighter even though it may not affect bandwidth. So a lot of triode amplifier designers don't use it because they can get smoother sound.
So there is a lot more here than just operating a pentode in triode mode!