Ultimately only Steve will know what kind of load it would place on the game. We could go back and forth all day but it would be just as useful to guess the color of his socks.
Here are some numbers to give a general idea of the damage reduction that would take place with different armor levels (all are approximate, and at 5% block chance per layer):
20 layers: 36% no blocking, 36% 1 point, 20% 2 points
15 layers: 45% no blocking, 36% 1 point, 13% 2 points
10 layers: 60% no blocking, 32% 1 point, 8% 2 points
6 layers: 72% no blocking, 24% 1 point, 3% 2 points
5 layers: 76% no blocking, 21% 1 point
4 layers: 80% no blocking, 18% 1 point
3 layers: 85% no blocking, 14% 1 point
2 layers: 90% no blocking, 10% 1 point
So for the most commonly used armor layers (1-6 or so) there isn't a huge change. If you compare worst case (all x1) vs. best case (all in one strike) the difference is 15-20%. Is that huge? If you want to use AMMs as ASMs it certainly is significant as you have to build the missiles, haul the missiles out and actually get them through whatever active defenses your opponent has. If you're using a Gauss cannon, max-range laser or some other similar weapon I doubt it. Oftentimes you outdamage the enemy significantly (jump points, planets) or simply outrange them in a fighting retreat. Since you aren't hauling ammo and you have time the 20% shouldn't be a problem. If you're in a real fight the rules apply equally and it only hurts the ships with little weapons which are probably outranged by bigger lasers or railguns anyway. When it really becomes big is when you have a dozen layers of armor, but at that point it seems reasonable that a fast-firing light cannon like a Gauss cannon would have trouble against such a big and heavily armored ship. It still does do damage but it's less effective, point for point, than a bigger weapon.
Those are my impressions from my games at least. It seems to support how I think combat should go and doesn't unduly restrict most weapons.