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Why are there 6ohm cabinets

It won’t hurt anything. Your cab’s ohm rating can be higher than your amp’s ohm rating (so plugging in an 8 ohm cab into a 4 ohm amp is fine). But you don’t want to do the opposite... never connect a 2 ohm cab to a 4 ohm amp, or it will do damage.
No. It is the other way around with tubes. Less cab impedance than the tap rating is safer than more.
 
It won’t hurt anything. Your cab’s ohm rating can be higher than your amp’s ohm rating (so plugging in an 8 ohm cab into a 4 ohm amp is fine). But you don’t want to do the opposite... never connect a 2 ohm cab to a 4 ohm amp, or it will do damage.

This is true for SS amps. Tube amps are generally the opposite. Tube amps will tolerate lower impedance cabs just fine. Higher impedance cabs put more stress on them. Running a 6 ohm cab on a tube amp rated for 4 ohms probably won't be a problem. After years of use maybe you'd have to replace the power tube a couple of weeks earlier than you would running the amp at the stated impedance.
 
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So,there isn't any unwanted stress on a tube amp as long as it can handle 2-4-8ohm loads?

Yes there is extra stress on the tubes, transformers, and other components when you run an impedance mismatch. Whether you would be better of running the 6 ohm speaker off a 4 ohm tap or an 8 ohm taps depends upon how the amp loads the tubes. Some amps work better if the impedance is slightly too high, while others work better if the impedance is slightly too low.

If the amp maker is still in business, the safest bet would be to contact them and ask their advice.

Being as the mismatch is so minor, I doubt you will have problems either way, but you might get slightly more power and slightly longer tube life if you use the optimal mismatch.
 
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