I had a look at the "sub-miniature" Russian "6" series Triodes. As suspected they are not really suitable for Battery operation as the indirectly heated cathode with 6.3V heater takes 400mA. HT 100V
http://www.radiomuseum.org/tubes/tube_6n16b.html
That's 2.5W compared with 27mW for TWO x 1j24b pentodes (HT 50V), or 130mW for two of the higher power 1j29b pentodes (HT 100V)
Today for semiconductors the Cascode is one of the "best" RF front ends. I'd guess adoption was slower for valve Radios due to extra cost and the fact also that the idea of the circuit was not widely known till well after Pentodes available.
HF is noisy anyway. Noise level received by aerial drops with rising frequency so that at Band I, a NF of 5dB can be fine and 1dB at UHF. At SHF / Microwave the received noise is so low that 0.5dB is worth while. LNBFs with 0.2dB or 0.1dB NF are probably marketing fiction.
So there is little value really on LW/MW/HF of Cascode Triodes compared to Pentode. It's for Instrumentation Amplifiers and low o/p Magnetic cartridges that a Triode should be lower noise than Pentode (the Pentode 1/f partition noise), not at 2MHz to 30MHz.
The cascode circuit reduces the effect of the "Miller" capacitance (grid/Anode) as the upper stage is essentially grounded Grid (makes capacitance be on o/p instead of to input) and makes the 1st grounded cathode stage have a load impedance that migates the Cag. At least I think that's the theory. This is why a Pentode with G2 suitably biased and loaded and not decoupled and G3 decoupled at RF is regarded Analogous to a Cascode (the G2 is equivalent to V1Anode / V2Cathode and G3 to grounded V2grid). At least that's what I was told many years ago.
Certainly I found in testing the Sub-miniature Russian Pentodes that the "right" value of G2 load (with no decoupling), while reducing LF gain by 20% to 30% resulted in "flat" response and dramatically improved RF response. Also of course for such operation a much higher HT voltage than for "strapped" triode operation was required