Often, the choice of a triode-connected pentode instead of a regular triode is based on availability of a particular set of parameters.
Triodes are usually preferred for low-noise applications because they do not have "partition noise" that occurs in tetrodes and pentodes due to the cathode current randomly dividing between screen and plate.
Usually, the only downside of a triode-connected pentode is that the screen-cathode voltage rating is typically lower than the plate-cathode voltage rating of the pentode, and thus possibly lower than that of a true triode of similar dimensions.
With a pentode, in either connection, the gm referred to cathode current depends almost entirely only on the screen voltage, where the dependence is that of a triode.
The original Neumann U47 selected individual Telefunken VF-14s for noise, grid current, and its good microphonic behavior (only one microphone in the package, please!), but that tube went out of production. Neumann operated it at lower than normal plate and heater voltages to extend its lifetime.