It seems that players rush back to the field, and lie about injuries, because they worry about losing their jobs to injury. Would guarenteeing contracts lessen the incentive to put their health in danger?
Yes. It would also lessen the incentive for them to play at all.
As it is, the phenomenon of a guy playing well, getting a huge contract thanks to playing well, and then proceeding to play far worse, is far too common. I think it’d be even worse if contracts were guaranteed.
Players can’t be cut from the team if injured, and must be medically cleared before a team can cut. Players probably fear the next man out-performing them and being made expendable.