Well, with a tube using a CCS for its plate load, the impedance presented by the CCS will be in parallel with the internal plate resistance (rp) of the tube and the following load resistance.

With a triode, which has low rp compared to the CCS, the result is that the output impedance of the triode stage will be the triode's rp in parallel with the load resistance. Any variation in rp will be apparent to the load. That's all great, because the triode's rp will determine the output impedance, and can be made to be much lower impedance than the load. The triode will be more lightly loaded with a CCS plate load than if it had a resistor plate load. The triode achieves more gain and lower distortion with a CCS plate load.

With a pentode (or a cascoded pair of triodes), which has as high impedance as the CCS, the result is that the output impedance will be very much higher, perhaps more than 10X higher. A typical small signal pentode's rp is about 500k to 1M ohms. The CCS impedance could also be about that (500k to 1M ohms). The following load resistance might be 500k ohms. That means the output impedance could be something like 165k to 300k ohms. If the load has significant shunt capacitance, for instance the Miller capacitance of a fully-bypassed 12AX7 or an RIAA filter network, that high output impedance will be in series with that shunt capacitance, forming a low-pass filter, causing loss of high frequency bandwidth.

With a resistor as the plate load of a pentode, the value of that plate resistor becomes the output impedance of that stage. If we take a 6EJ7 (EF184) and install a 22k ohm plate load resistor, that will be in parallel with the (high) rp of the pentode and with the (should be high) value of load resistance. The result is that the output impedance will be close to the value of the plate load resistor, which is a lot lower in value than the rp of the pentode.

So, my concern is limited to pentodes and cascodes, and has to do with output impedance and how that will affect bandwidth, not with gain and distortion.

Also, keep in mind that the PSRR of a pentode or cascode is many times worse than that of a triode. With a CCS loaded triode the PSRR gets close to the mu of the triode. What does a CCS plate load do for the PSRR of a pentode or cascode?