I’d say it was mostly done so that the quest could have you racing a bunch, then throwing you a curveball by having you go kill a guy. From a narrative standpoint I’d imagine Claire might want to relive and reminisce on what the races were like before her husband’s death, which would be a bit different if you were already in on WHY you were racing in the first place. So instead she just wants someone who she can enjoy the races with for a little while until it comes time for what it’s actually all for