Another factor is that the injury doesn't even have to be "serious" to cause issues. Just think of Fields relatively minor knee injury, and if he was eligible for the 2020 draft. He would've had ~6 months to heal prior to OTA's starting (which are most crucial for Rookie QB's).
If that same injury occurs in April/May, you're talking about only 1-2 months before OTA's start, in which he might not yet be 100%. A knee tweak, a deep bone bruise on the throwing hand, a pulled hamstring, a sprained ankle, etc... could all set you back heading into your rookie year. Those minor, and common injuries are not a concern if the season ends the first week of January.
Plain and simple. In a fall season, the only injuries that are concerning to the NFL are bone breaks and torn ligaments/tendons. In a spring season, the list of "concerning injuries" increases exponentially.