Then I had a blinding epiphany that left me stunned and gasping for breath so that I had to go and have a bit of a lie down.
In an abstract game combat system, where a round of combat represents an exchange of blows, parries, and offensive and defensive maneuvre, there is absolutely no point in wasting time and dice rolls on determining who goes first. All that matters is determining how much damage a combatant can dish out over the course of that round.
That's already dealt with in the hit+damage dicing system. Roll to see if you manage to do any damage at all, and if you do manage to damage your oponent over the course of the combat round, roll to see how much damage you achieve. Fighters with multiple "blows" simply have a greater damage potential within the combat round's time-frame.
Even six or ten seconds in combat is a long time.
The surprise roll, now that's still useful in an abstract combat system — being able to do damage without taking any in return is basically what combat tactics are all about. I'd definitely retain the concept of a surprise round; in fact it would become even more important if initiative were removed from the equation.
Where an initiative determination system is valuable is in a system where one combat round equals one blow (or grapple, or throw, or whatever). Then it actually becomes important who goes first and who has to react. Otherwise — it's a waste of time.
NOTE: It has been pointed out to me that the initiative roll has a valuable dramatic impact on D&D combat — that's a valid point, and I concede it. It's probably worth retaining for that reason alone. I still think it's structurally pointless though .