Cathode impedance is low and non-linear.
Two cathodes "fighting" each other will give a gain of half; no better than a passive 2-resistor mixer; however input impedance may be higher.
The maximum output of your plan, assuming 300V and 12AX7, is slightly over 1V peak with 5% THD.
For very large signals, whichever input is more-positive will swamp the other input. Distortion is gross. It may have use as a "fuzz"; there may be cheaper ways to fuzz.
The plate-mixer has a similar issue, but not so bad, and with significant gain. Clean output may be over a dozen volts.
The 2-resistor plan has no maximum level or intrinsic distortion, except that whatever the sources can do is divided by 2 (if a source cam make 50V clean, the mixed output may be 25V). The resistor value is a compromise. Values below 200K load typical sources, values over 200K shave the highs. The Designer has considerable leeway: you find 100K and 470K mix resistors (and 3.3Meg:220K when an unequal mix is wanted).
If you can accept 2:1 loss of gain, can accept ~~270K mix input, then 2 resistors is the simplest plan.
If you can't spare the gain but can drive resistances, use fairly large (330K-470K) mix resistors to a single triode hobbled for low gain (ideally "2", but since you have extra you know you'll want more).
If you must have very high impedance mixing without loss, you are probably into some form of 2-triode plate-mixing. For maximum clean output, don't tie the plates together, use two mix-resistors after the plates.