Received my tubes yesterday; on close inspection the phosphor coating appears thin (it's definitely not opaque). My guess is that the low anode voltage (only 500 volts, versus typical of a few kilovolts for scopes) results in relatively low-energy electrons, so if the phosphor is too thick it might make the trace less-visible. Most likely, I will try NOT to focus the beam too sharply, and paint single-digits on the tube, like a NIMO, rather than a clock-face, or multiple digits, with sharp features, The price of a 3L01I is certainly much lower; 15 USD for a tube compared to a recent auction for 2 untested NIMOs that sold for 650 USD.
I know that older color-TV picture tubes (eg, 21FJP22) had a rather thick phosphor coating because a friend of mine lit a fire inside the tube and we could barely see the flames, or the several gallons of water we poured into it to put the fire out....Not to mention how thick the glass is across the face (we had to use an axe to break it up on his front lawn).
I also think the writing-speed of TV tubes is significantly faster than the 3L01I, so it likely requires higher current.
BTW, does anyone know what the anode-current spec is for a 3L01I ? I did not see it mentioned on the datasheet.