I just did a quick check in my worlds that have played a significant amount of games(a couple are 40 games or less into the season). With one exception, the owners plunking 3-5m into a FI are also losing a ton of games. While FI has no effect of how your team is playing(and I'm sure someone will say "But they're developing their prospects!!!"), it does affect where you can put your funds. For the most part, those same owners haven't had a lot of HBD success. Don't know if there's a correlation but it seems to me that worrying yourself over making sure your FI is comparable to your HC/PC, ratings-wise, might be a strategy for losing.
I've got an 80(630k), 69(750k), 56(500k) and a 63(508k). I don't feel as if I'm losing a thing by not paying 3m for a FI.