It's a case of diminishing returns.
If you can already kill something in one shot, killing it MORE in one shot is pointless.
If things already can't do any damage to you, then doing even less than none damage to you is similarly pointless.
The vast majority of games - tabletops too - do not have weapons and armour equal. A better offense means you will take less damage in total, contrasted against the armour. Look at it mathematically.
Scenario A: When Armour Is Better
You are fighting opponents. They have 1000 health each, and deal 50 dps. You have 2000 health and deal 100 dps. [Numbers grab-bagged for maths!] Assuming you fight them one by one, you can take out 3 before you should to stop and heal. If you increase damage output by 10 dps you gain a full 50 hp back. This means you can riskily fight four. By increasing hp by 10%, you can now fight a fourth before stopping to heal - after those first three, you have 700 hp left, and it only costs you approximately 500 to take one out.
This is also not taking into consideration that healing may require its own resources, which will be covered in:
Scenario B: When weapons are better
You are fighting opponents. They have 100 health each and deal 20 dps. You have 100 health and deal 20 dps. Assume damage is constant and damage packets occur once per second. Without an equipment upgrade, you are not going to be successful fighting these opponents.
With the armour, you can suddenly have 200 health instead of 100. This means you can take about one on. It would be too risky to try a second, but you may try it (especially if you know the first hit is yours), as the equality of the ratio has shown itself. 200 vs 100, 180 vs 80, 160 vs 60, 140 vs 40, 120 vs 20, 100. Assuming the other side got the first hit in. Statistically, you're at the same likelihood as the dps-focused in this scenario, but you're less likely to get the first hit in (as armour tends to be on the slow side) and you're psychologically shaken as your big tough armour guy is at half health, maybe he should heal up a bit.
With the weapon, you can suddenly have 40 dps instead of 20. Now, if you can get the first hit in, you can actually take on another fight: 80 vs 60-> 60 vs 20 -> 60. 60 vs 60 -> 40 vs 20 -> 40. A third is too risky, but as long as you get the first hit in one of the fights you're good. Furthermore, as recovering health requires resources (time, gold-from-loot, getting other people to heal you, your own energy/mana pool, whatever) you are expending less of THAT recovering your own health. Very nice.
On top of this, you killed two opponents in 6 combat rounds, or 6 seconds. The armour killed one opponent in 6 seconds, and took much more damage while doing so. Not a good trade.
Furthermore, eventually those 100 hp enemies are going to scale up. When they become 105, 110, 115, or 120 hp enemies, the armour guy will take a hit as now he has to go another combat round, forsaking his chance for a second kill. The weapon guy won't even notice that they take longer to kill, and will only notice if their dps goes up.
Lastly, if armour instead decreases damage coming in.
If the enemy has 100 hp and is supposed to do 40 dps but only does 20 dps.
A 100% increase in mitigation turns it into 10 dps: essentially doubling your hp. Look at how well that turned out last time, in comparison to the 100% increase in damage. The difference being in that healing to full no longer costs twice as much.
Most games will reward the increased damage by a fair bit more; from D&D to 40k to Mass Effect to Guild Wars. You simply get the rewards for victorious combat faster and therefore can spend the fruits of your labour in a more time-efficient manner.