A player is consulted with before designated to I.R. They could have a long fingernail and be put on I.R. as long as both sides agree.
A player can file a grievance if they feel they are not injured. From there the player would have to pass a physical by league. The team would have to reinstate player, move player to practice squad or cut player.
If the player gets moved to practice squad every team has the ability to pick them up if they will move the player to their starting roster. Some teams put players on I.R. vs cutting player simply to make sure no one else can use him.
Now if a team cuts a player, they might have salary cap or contract issues to face. If the player has guaranteed money it will all go to next year's cap. The player might also have guarantees on annual compensation. So then you would be cutting someone you will pay fully anyways. You might want the player around to see how he looks during rehab. Last thing you want is to have a need at his position and wonder what he was doing the past 8 months.
Also a few other things to consider. When a team cuts a player, they may lose overall good will in the league. No one (agents too) wants to sign a contract with a small bonus knowing that this team likes to cut players. So the move could potentially cost the team.
Another factor is that if a player was hurt, no matter how small, and they are cut then there are usually some legal issues. Basically the two sides have to come together for an injury settlement. This happens a few times a year at least but pushes bad will out on both sides. The team looks like they are casting off the injured and the player looks bad for collecting money for no play.
The truth is IR is a bit of a joke. The new rule allowing for a couple of short term IR exceptions helped but IR still is a joke. Some rosters are loaded. So teams that want to keep a players rights throw them on IR - player agrees so he doesn't get cut. It is kind of like a redshirt year. Also on really bad teams you might have little to no depth at a position. Well you can only have so many inactives... well now a guy out for 4-5 weeks is gone all year.
The rules were put in place - short inactive list, 53 man roster, IR rules - so that teams couldn't hoard borderline players and so that talent was better dispersed. To a point the rules might help a little but IR is used more for circumvention.