The league mandates the equipment though. It should be incumbent upon the league to ensure that the teams have the chance to have operative equipment during the game.
If an NFL technician found the equipment to be in working order, teams could be penalized one of their three timeouts, a challenge, or cash, depending on how egregious the infraction was.
By your logic, teams might fake injuries to give themselves free timeouts. While that may indeed happen, I don't think we should make the rules with that assumption.