Why are/were there almost no tricycle-gear biplanes?
It is a bit more than a coincidence. You might also ask why there are so few biplanes with retractable landing gear. The reason is similar.

Biplanes are propeller-driven (except for this one), and in almost all cases the propeller is in the front. Efficient propellers are large and require a longer landing gear when a tricycle gear is used. Granted, the plane will lift its tail during the ground run so the prop comes down a bit, but that happens over a flat and clean area, so lower tolerances can be afforded during the ground run than during all other ground operations.
Tricycle gears produce substantially more drag. The nose gear sits directly behind the propeller and in its slipstream, so its drag contribution is typically 40% of the whole gear drag. Tricycle gears became less of a drag (pun intended) when gear retraction became standard.
Biplanes are built light and the heavy engine cannot have much distance to the center of gravity. Where do you mount the nose gear? There is preciously little room for another piece of structure. And once that nosegear is crafted on the plane, its distance from the main gear is rather small. Any bump on the field will produce strong pitch oscillations when hit by the nose wheel. Better to have a tailwheel or skid at some distance from the main wheels.
Tricycle gears became a necessity with higher wing loadings and higher landing speeds. Biplanes don't need powerful brakes. On the contrary, on a grass field a taildragger is easier to handle. And with their short ground runs, biplanes often operate from grass fields.

Not that tricycle gears weren't tried. See the picture of a Breguet 6 below (source), conveniently proving that pusher biplanes were also designed. Gun synchronisation removed the last reason not to place the propeller in front.