The loss of granularity is certainly something you'll feel.
You could make it strictly comparative, and also take shifting into account:
By default, everyone has a Reach 1 and can use their move to Shift 1.
You can attack an enemy in melee without engaging them if your Reach is greater than their Reach.
You can engage an enemy who's reach is greater than yours if your Reach + Shift is greater than their Reach. Otherwise you follow the rules for disengaging (I can't recall the 13A disengage rules, exactly, ATM).
In some ways that's better than 4e reach (a bit like 3e reach or threatening reach), but it's fairly simple.
You can disengage from an enemy automatically if your Shift is greater than his Reach.