You only get 4 seasons with these guys anyway, if he misses one season he's lost 1/4 of his value right out of the gate.
I don't think that's the right way to look at it. First of all, most players don't start or even contribute much their rookie years, so equating a rookie year to an equal value as 2nd, 3rd, and 4th years is a bad way to look at it. Those years are more valuable for almost every player.
Secondly, you'd like to hope you are drafting players it would make sense to give a second contract to. If you let all your draft picks walk after their first contract is up, they probably weren't that great of picks.
Third, if a guy misses his rookie season, then went on to be a solid starter his second and third years, then made the Pro Bowl his fourth year, then walked in free agency, you are actually gonna tell me that was a bad pick in the fifth round because he "lost 1/4 his value right out the gate"? Who gives a shit at that point?
You play to get quality starts out of these guys, not time spent on the active roster. I'll take a player I feel is going to be able to give me those quality starts down the line ten times out of ten over a player who is just going to be a healthy warm body.
This is the same logic that would say David DeCastro was a bad pick for the Steelers because he "lost his rookie year due to various injuries."
Uh.... yeah.... except he was one of the best guards in football his sophomore year and is just gonna keep getting better. So...uh.... that argument doesn't amount to much.
A highly-regarded player missing his rookie year is no where near "losing a quarter of his value." It's a small though notable detriment, which is going to be outweighed by talent, if the player is the hands down BPA, nearly every time, notwithstanding whether the you feel like the injuries will be ongoing (like in Leary's case).