Depends what you mean by light and heavy.
https://www.youtube.com/watch?v=HagCuGXJgUs has a crossbow firing 6 shots in 51 seconds, so that's about 8-9 seconds per shot. It's a quite light crossbow with a draw weight of 130 lbs that can be cocked by hand with just a foot brace. In terms of power, it's probably on par with a short bow, nowhere close to a long bow. But RMSS's light crossbow is almost on par with a long bow for damage and crits, well above a short bow. To me that suggests that "light crossbow" should be something considerably heavier that might need a tool to cock, while a "heavy crossbow" needs a crank of some kind. (Although in fairness
https://www.youtube.com/watch?v=iIkxyjVu9gc shows a goat's foot with a 300 lbs crossbow not incurring much speed penalty.)
RMSS puts loading and firing a bow as something that can be done in a single round (with a penalty), while loading and firing a light crossbow is 190-220% of a round, so it can be rushed to fire every other 10 second round. (Heavy crossbow is 250-280%, so every third round.) Those do seem a bit slow.
RMU permits a bow to fire every round, or even twice per round with a penalty (1-3 AP plus 1 AP to load), while a light crossbow takes two rounds to load and fire (6 AP to load plus 1-3 to fire, with 4 AP per round), and a heavy crossbow takes four (14 AP to load plus 1-3 to fire). But rounds are only 5 seconds long, so that's a bowshot potentially every 2.5 seconds, a light crossbow every 10 seconds, and a heavy crossbow every 20. Those don't seem unreasonable when you factor in some chaos of combat vs a safe, fixed target shooting environment.
For real speed shooting, you can also add in adrenal speed and combat styles. E.g. the RMC Combat Companion has styles that potentially halve the loading time of bows and reduce the loading time for crossbows to as low as 70%, while the RMSS Martial Arts Companion gives a lesser boost of only 20% (which doesn't make much difference for a crossbow). The fighting styles in the RMU Character Companion will permit reducing the loading time for light crossbows from 6 AP down to 3 (permitting rushed shots every round), and heavy from 14 AP down to 10 (permitting rushed shots every 3 rounds). So don't compare the base speed rules in any of these systems to the fastest shooters, they should be considered "typical" rather than exceptional speeds.
Extremely simple rounds (e.g. a 2-second round where you get one action per round) don't provide much room to accommodate differences between different weapons. Shooting an arrow every 2 seconds is possible if you are very, very good but it's rushed. I couldn't do it, not even close. Whereas it's hard to even imagine using a weapon where you spend 9 rounds out of every 10 just loading (for the heavy crossbow), that's not any fun to play. Even a light crossbow firing once per 5 rounds is just going to fail the fun test. Both RMSS and RMU let a light crossbow fire every other round, that's paying a cost but at least it's playable.
Personally, I've used a crossbow for SCA heavy archery. Mine has a ~105 lbs draw, which is quite difficult to cock by hand unless you are wearing a rigid breastplate to brace it against and have big armored guys running at you with weapons drawn. Then it somehow becomes pretty easy.
But compared to something you would want to use in real combat, it's pretty light.
One thing I did find with a crossbow in combat -- and this applies to bows too -- is that you spend more time than you would think trying to line up a shot, especially if you are shooting from the second rank. I think a realistic way to handle this, which I don't think any game does, would be to say that at least some of the time when your attack roll is a complete miss (but not a fumble), you actually aren't even firing a shot, you are simply still trying to line one up. That would increase how frequently you could make attack rolls without implying unrealistic loading speeds (since you would be able to make your next attack roll without needing to spend any time loading).