It's pretty clear from research I've done on other teams on my level increasing squad numbers is not the answer, clubs with smaller squads receive less injuries.
There has to be a multiplier in the game engine that takes certain factors into account to make the leagues and comps competitive.
IMO they are squad numbers, skill levels, over training and when players are close to gaining or completing a skill level, where the engine deems his progress to quick.
Some of the stats I've been monitoring on my own team.
Last season maximum games played in all three competitions.
Since the start of last season, to day 7 current season
Injuries 25.
Avg time of injury 8 days due to two broken legs
Game days played 35
Player days lost 200
65 games played in total.
Equivalent games missed by injuries if applied to one player, 394 as some days there are only single matches, roughly 7.5 seasons.
22 man squad reduced by 5.7 players per day. If you don't use medic packs.
Using medic packs if bought at an AVg of 12 per injury, 300, 276 tokens.