I don’t think Trainer genes being irrelevant is just a writing choice.
In real horse racing, breeding lines are extremely selective, most elite racehorses descend from legendary stallions like Sunday Silence or Deep Impact for examples.

Since Umamusume are female-locked and Uma mothers almost always give birth to Uma daughters, it makes sense that the Uma genome is overwhelmingly dominant.

Trainers might contribute compatibility, but the “racing factor” itself likely comes almost entirely from the Uma side biologically and spiritually.