At the moment each side can use 3 substitutes per game. For the English premiership that is 114 per season.
How about changing it to a system where they start the league season with 114 and use them as they see fit. When they are done they are done. It would allow coaches maximum flexibility during a game in the knowledge that they would have fewer available at the end of the season, or they could them up for the end games.
If we followed your idea, Newcastle's season would come to an abrupt halt in mid-October, leaving thousands of members of the Toon Army free to wreak havoc in the Bigg Market every night of the week, not just Friday and Saturday.
Use a similar system to that used in rugby league - in that sport of 13 a side, 17 players are named for a game and the manager can interchange between them 10 times during a game i.e. at any given moment of the game any 13 out of the 17 can be on the field of play. That way a player can be given a rest for a few minutes and brought back on later, or the formation can be changed several times during a game by changing the personnel.