My personal view is that only Covid cases should be taken into account when considering postponement requests, not injuries. Injuries are just a part of football and will happen to all clubs, and allowing clubs to get out of games because of them just doesn't create a level playing field. As an example, if the Everton vs Newcastle game tomorrow hadn't been called off Newcastle would have been without their only real goal threats. Chances are when it is rearranged one or possibly both of them will likely be available, that isn't just unfair on Everton but also Newcastle's relegation rivals. Conversely Leicester had to play their game at Man City with only one recognised centre back, and two midfielders playing in the back 4. Different competition, but Sheffield Wednesday had to play a recent game with a full back (who is really a midfielder), a striker and a left winger as their back three.
You would hope it wouldn't happen, but there is the obvious problem that some clubs could use it to their advantage. As a purely theorical example, if Liverpool were due to play Man City and had Salah, Mane and van Dijk out injured, could they manipulate their injury numbers to avoid having to play the game? With Covid cases the EPL could ask to see evidence of positive tests, but they can't do that for injuries as that is down to the club's own physios.
Almost every club has a U23 and U18 squads, so they really should be using players from those to make sure they can field a team. Which is what, as another example, Liverpool had to do when they lost all of their centre backs last season.