Beyond Shirogane's lack of a strong drive/dream to race, I think there's something even bigger holding her back, something unthinkable for an uma: Tanya cannot see racing as something precious, something that truly matters.
Think back to Chapter 5, and how Shiro's reaction to Steady Distance's high stakes win is...disinterest. She doesn't belittle Steady's victory, and is happy for her friend, but to her it's just an achievement like any other - something to be pleased about, but nothing more than that.
Tanya sees value in racing, but only in terms of its social/economic benefits, rather than something valuable in itself. She enjoys races in her own way, but they're just one of multiple things she likes, not something she sees as a lifelong passion. If forced to be entirely honest, she'd probably admit that there are careers she'd prefer instead of racing.
This disconnect, in my opinion is an even greater hurdle to her future as a racer than simply forging an ambition to win. Because at the heart of it, races aren't important to Tanya in the way they are for other uma. She'll seek victories to ensure she has a stable income and for her own pride, but her life as a racer doesn't actually matter to her, and that's the foundation for racing.
I think her trainer and comrades might gradually pick up inklings of Shirogane's divergent view of racing - when she treats reviewing old races as more of a tedious homework than her actual "leisure" homework, when she doesn't show particular excitement one way or another in others' races or her own. But it's probably going to be hard for them to piece together, and will hit them all the harder with shock if they even reach the revelation.
Because from what I understand, this disconnection from racing is a fundamentally alien perspective for an uma to have. Uma are born to run - partially in body, but more deeply in spirit, reborn from souls that wished with all their hearts to race once again. But Shirogane was born from Tanya, with no such dream fueling her at the core. Racing is just something to do like anything else, and that disconnect makes me all the more curious on where her journey as a racer will carry her.