Almost all encounters should begin with a Surprise Roll to establish Party/Monster awareness. Surprise needs to be established first, because all other rolls are dependent on determining the state of awareness (Encounter Distance, Reaction Rolls, Attack Rolls, and so on).
Establishing Surprise can make combat a much riskier prospect (even for high-level play, a round of Monster Actions without preparation can be deadly) and ignoring or hand-waving the potential for Surprise rounds can potentially downplay player actions and decisions.
Other uses for the result of Surprise Rolls
It's Side-Based Initiative
Surprise already determines “who gets to act first” in situations when one side is surprised. In the event of “neither side is surprised” or “both sides are surprised” re-purpose the dice as the initial Initiative Roll. Or if you don't like ties, on Even sums the players act first after Surprise is resolved, if the sum of the Surprise dice is Odd, monsters act first. The 2d6 bell curve makes 7s more common, so Monsters will typically act first. Maybe do Odd = Monsters in Dungeons (home turf advantage), and Odd = Players in a more level playing field.
It's Encounter Distance
Encounter Distance is probably the most frequently ad libbed, overlooked, or hand-waved determination in older D&D. Since it is often directly constrained by the map in a Dungeon Environment, many DMs ignore random determination of Encounter Distance for planned encounters, or only use it for Wandering Monsters. The table look up required probably contributes to their disuse.
Encounter Distance is important because it directly influences the Combat Options available to the parties (Missile and Spell Ranges, Movement required to Engage in Melee, Weapon length, etc). Tactical decisions are player choices that shouldn't be minimized by fiat. It could also be said that the need to establish Encounter Distance before Reaction Rolls is important, as some forms of communication may be more challenging or impossible over longer distances.
Conveniently, Base Encounter Distance (Indoors/Dungeon in Dim light) is 2d6 x 10'. Use the 2d6 that were rolled for Surprise. Change the feet to yards outdoors. Halve product for No Light, halve it for Surprise, double for Very Good Light. While the ranges produced by this method don't match the Rules Cyclopedia exactly, they are close and much quicker than performing a table look up. Lower Bound is 10' (for Surprise in No Light), Upper Bound is 240' (Very Good Light, No Surprise, just barely in the longest Missile Range on the standard equipment list, the Heavy Crossbow).
It's the Reaction Roll
Blasphemy! But consider that a low sum of the Surprise 2d6 are probably surprise situations, which are not necessarily conducive to diplomacy, as the surprised party often reacts physically. In non-surprise situations the Surprise dice would be discarded anyway, so use them for the reaction roll.
If you re-roll Side-based initiative with 2d6 every round, consider folding this into the 2d6 Morale roll. This way Initiative is only redetermined when the tide of battle changes (the triggers for Morale Checks work well to reflect a change in the battlefield).