If you're gaining 2 edge on your attack, armor already HAS done something: the NPC not wearing enough of it has given you an edge point.
And in such a case, yes your armor can't give you more in the same round, but it can still deny edge to your attacker. Armor is edge denial. Yes, not helping soak is a big change, but helping prevent edge actions from being used on you is still a big benefit.
Except that
denying Edge can be very often be done with Body alone. There is a band of 8 Points of AR-DR difference in which nothing happens. Remove the benefit for having a DR thatīs 4 points higher than AR (or vice-versa), and you have a margin of 8+ points in AR-DR difference until the outcome flips from "no one gets Edge" to "your opponent gets Edge". Itīs a massive loss in verisimilitude.
Thatīs why I think that there also should be more than 3 outcomes (A gets Edge, B gets Edge, no one gets Edge) resulting from the AR-DR comparison.
Just have look at the DR of the Steel Lynx for perspective. 10 Body plus 16 Armor for a DR of 26! Is that even RAI or did someone accidentaly put in the originally intended total DR in as the Armor Score?

Anyways, a DR this high high is possible with the right perks and good cover. This is way beyond any AR that can be fumbled together, so theres not difference if the Attacker uses a Anti-Material-Rifle or a Pistol, apart from the Damage Code. If the DR-AR difference is really extreme, there should be an additional benefit for the dominant character. Likewise, if the DR still has (if just a little) effect when the difference is lower than 4, it would add another incentive to watch these ratings whithout making the game too complicated.
Suggestion: - AR is 10 points higher than DR: Defender canīt spend Edge on the defense (will happen rarely, but itīs possible)
- DR is 10 points higher than AR: Attacker canīt spend Edge on the Attack (will happen a bit more often)
- If the Attacker and the Defender roll a draw, use the DR-AR difference to determine who wins/hits (afaik, attackers hit on a draw in the current RAW). If these values are the same as well, use ERIC (Edge, Reaction, Intuition, Coin toss).
Meaningfull, yet easy to remember. Instead of 3 possible outcomes from the AR-DR comparison, you have 6 (even 7). These new effects are also not affected by the 2-Edge-Limit.