I think the afterburner idea is not a good one. It would just mean adding tedious micro with no real benefit/drawback, not to mention it would be out of line with how units normally function. (Most units do not have special abilities that require constant management.)
If the afterburner provided a speed boost, that reduces the amount of time that is required for planes to get from their construction point to an engagement and makes planes less vulnerable to ground AA that they fly over en route. It would serve pretty much no other purpose, because it's not like you could use your afterburners to run away from a losing engagement - your opponent has afterburners too!
Reducing the time to engagement rewards players who poorly position their units, whilst punishing players who use feints, diversions, and other good placement tactics. Why is this desirable? Making planes less vulnerable to ground AA during flyovers further reduces the effectiveness of ground AA versus aircraft and rewards players who do not bother to scout the enemy's AA ahead of time or destroy it to make way for a bombing run. Why is this desirable?
If the afterburner provides a maneuverability boost, I am skeptical that it would provide any benefit at all. Your opponent will simply use his afterburners as well during an engagement, so the only likely effect I can think of is that engagements would result in less destroyed planes as each player's aircraft have a harder time hitting and must disengage to refuel sooner. Why is this desirable? It changes the gameplay a bit, sure, but how does it
improve it? It would also give a player who is defending an advantage, because they can drop down, refuel, and leap back into the fray, whereas an attacker cannot. Isn't giving the defender an advantage what ground based AA is for?
In either case, it would create a situation within the game where players must be on the lookout for whether or not their opponent is using afterburners so that they too can activate their afterburners to negate the advantage. I believe I already said something about "tedious micro"?
People seem to think that airplane fuel does not play a big enough role in this game, and should be a greater factor, but I disagree. Look at how you run land battles in open spaces - you have your cluster or clusters of units, and they move into engagement range of the enemy units, trying to destroy as many as possible from the edges of their formation before retreating and regrouping, and you use your intel to avoid where their concentration is greatest, attacking the flanks. In 20x20 or smaller maps, you do not see this method of play with air units. Whoever gets the greatest concentration of airplanes controls any part of the map where their opponent does not have lots of AA, because a group of ASFs can, realistically, reach almost any point on a 20x20 from almost any point in under a minute. You cannot outmaneuver an enemy's airforce to any significant degree. So of course most player don't normally see planes needing to refuel, they're either in combat or patrolling over the base.
If you play on an 81x81 (or some 40x40s) you will actually see fuel becoming a significant issue. The fuel time on an ASF is sixteen minutes. When it takes eight to ten minutes for a round trip to and from enemy territory, you are left with little time to loiter and/or fight before you must return to base. This makes staging or carriers essential, because you cannot maintain air control to pave the way for an assault or prevent an enemy breakout with an airforce of 50% hp planes at eight minutes of fuel remaining. If you want to see fuel being important, play on larger maps.
In any case, units is Supcom are supposed to work as advertised. They are not supposed to be tied to other units in order to function. This goes for airplanes too, so while some of these ideas to make fuel a bigger factor are good ones, let's not get carried away. This isn't supposed to work like StarCraft, where a plane is just a weapon deployed out of a staging facility, rather than a unit in its own right.