To @ScottHue’s point, it’s not really a race unless there are other uni riders that have similar skills.
IMO, riding a 36er in a small-time 5k/10k is not competing at the same level. Any average uni rider can ride an ungeared 36 at 10mph, given decent road conditions. At 58 with 4 years of riding experience, I would be whooping most of the 25 yo field.
I wouldn’t mind riding in some small, local foot races, but to level the playing field I would probably want to run a smaller wheel. By having less of a speed disparity there would be fewer opportunities for spills and accidents, which is a concern of the race organizers.
The biggest objection I have seen with getting race directors to let uni riders on the course is liability insurance and, to a lesser degree, the perception that unicycles are for the parades and circus acts.
In small numbers, I think unicycles in foot races could add another dimension to the event, perhaps give it an “oh wow” factor. It would be on the uni riders to recognize that this is more for fun, sort of a group ride, than it is a race.
I find that from a biomechanical perspective, unicycling is closer to running than it is cycling. But because we are a “cycle”, we are more likely to gain admittance to a cycling race than a foot race. In cycling events, unis are the under dogs. In foot races, we have every advantage, even on smaller wheels.
Since there are very few uni riders close to my home, I usually ride with cyclists. I have had the occasion to ride with runners. With the exception of the occasional diversion from the road onto some cart path, riding with runners is much easier, even on smaller wheels.
The ideal situation is to have enough uni riders to form a uni-division, and have a separate start time from the runners. The problem is there are so few uni riders. It takes 6 months of planning to gather 20 riders for a trip into the woods. Getting enough for a division in a small-time race, whose purpose is to raise money for a cause, is nearly impossible.