One way you could re-introduce such a spell would be to put conditions on it, e.g. it will only work if the character has loss less than 10% of their maximum Hit Points (minimum of 1 hp loss).
E.g. Bradden is a 5th level fighter with a CON of 14, his hit points are on average (10 + 5.5 + 5.5 + 5.5 + 5.5 +(2x5) = 42.
If he has suffered only 4 hit points of damage (less than 10% of his HP) Cure Minor Wounds could be used four times to heal those four HP.
E.g. Glub the 0 level commoner only has 8 HP, 10% of that that is 0.8, but with the minimum of 1 HP loss clause, it would allow that 1 HP to be restored as long as Glub has only lost 1 hp.
I.e. Cure Minor Wounds only works when the patient has suffered only minor HP loss.