Lower voltage and lower wattage zener diodes often don't clip hard enough. The number of diode pairs needed depends on the exact type and brand of diodes, since they can vary somewhat. Crossover distortion, bias shifting, even harmonics, etc. Other forms of distortion, if implemented, make the tone more like that of an actual tube amp but often not actually better. In most tube amps having adjustments that affect these, minimizing these effects is usually judged to result in the best sound.
Crossover distortion is affected by any control used to adjust the bias of the output tubes.
A higher bias favors less crossover distortion. When a tube amp is running clean, the negative feedback circuitry in the output stage largely corrects any effects of the output transformer. However, negative feedback only does this while reducing gain. During distortion, the gain is either nonexistent or less than the value the negative feedback circuit would reduce the gain to, and the negative feedback does not work. This makes the frequency response of the transformer become apparant during distortion.