It's probably worth pointing out that both City and Trade Route has increasing usefulness, rather than dwindling usefulness. That way you have to work or wait to unlock their power, rather than race for it, with the latter almost necessarily making the card swingy and luck-based.
What would the reverse be? Gain a card from a supply pile with just 3 or fewer cards left in it? That wouldn't be as bad, because the timing of when the race starts is in the hands of the players, so they could jockey for the best position to start the race. It also means the outcome of the race won't matter quite so drastically as (1) the game will be further progressed, when the impact of individual cards added to your deck isn't as great; and (2) with a bunch of cards gone from the supply pile already, it probably means all players already have -- or at least have had the opportunity to have -- a share of those cards.
I'm not saying that specific idea will work. It sounds super marginal to me, frankly, since by that point in the game you can probably just buy the card you want, rather than buy something to get it for you, and how often will you even be able to time your purchase correctly anyhow? I only put forth this variation to illustrate the point about swinginess and races.