I like the idea of group initiative a lot, but I do see some problems.
On one turn, a player could easily die and get hit multiple more times, becoming perma-dead before the players get a turn to heal. Normal initiative gives more opportunity for different players to try to save the day.
Along the same lines, under normal initiative, players have to be well-rounded: if somebody dies and it is your turn, it is up to you to save them, and you may not be able to wait for the "healer"'s turn. With group initiative, there is no reason to diversify.
What about this method? :
Readied Group Initiative
Everybody rolls initiative (P = player team). Roll once for all enemies (E). All who roll higher than the enemies get a surprise round (S). Game progresses: S E P (E P alternating until end of combat). During a team's turn, its members may take their turns in any order they wish.
However, all turns are readied by all combatants. Any time a member of the opposing team finishes a turn, a combatant may immediately spend its reaction to take its turn. Rounds reset at the start of the Enemy team's turn.