Indeed there is no minimum "useful" size limit. The 3-inch refractor/6-inch reflector concept was something Patrick More promoted. There was some sense in in though. I couldn't aspire to one when I was a lad, but I made great use of my 60 mm Tasco refractor.
Interestingly, in his "Starlight Nights", the great observer Leslie Peltier relates that when he was going to join the AAVSO in 1918 it had a minimum size telescope requirement of 3-inch. He was disappointed as his was only 2-inches. But when he filled in the application form, his letter 2 had an extra curlicule, making it look like a 3. He was in! And he became one of the most prolific variable star observers as well as discovering many comets.