The 3 subs rule didn't have a stupid restriction as to when you're allowed to make them though
If 5 subs are allowed then you should be able to use them at 5 different points throughout the game
I get the point that you're making and I've not fully decided either way, myself. But, 5 subs per team done separately means potentially 10 stoppages per game just for changing personnel. That's a lot of stop-starting, which I'm keen to see the back of.
The more I think on this, the more I think it's better to just have your 3 subs, plus maybe an additional sub when it's a game that has gone into extra time.
If we're that keen on doing 5 subs, maybe we could even organise it so that 3 subs can be made at any point in the game, but the other subs have to be made at half-time. E.g. 2 at half time and 3 in the second half.
Anyway, that's just me suggesting stuff and not really thinking it through fully. The rule is there for next season so we need to make the absolute best usage of it to our advantage. We are going to need it.