Yes, armor does allow more physical hits if obtained than HP does, but a few things to look at:

1. all heroes begin with a base armor, typically starting around 15 and raising 3ish per level. At a decent average of 30 initial armor (since early game is so important), 12.69 armor gives 42.69/142.69 - 30/130 which is 6.84% physical damage reduction. By my maths, 12.69 armor from 0 armor gives 12.69/112.69 - 0/100, or 11.26% physical damage reduction, so that's an important factor.

2. That's only looking at the physical damage, and not at burst damage from nukes, which is helped when you raise your HP.

This being the case, it's typically the best policy to pick either DPS, Caster, or tank, and mix effects from each of the helpful attributes for each. You can only get crit on Tryndamere. However, adding damage, attack speed, or armor penetration helps to improve damage he gets from his improved crit chance, instead of improving crit to improve damage over already fail stats. Though it doesn't look like it, all stats are diminishing to some point. You add 50 damage to a 50 damage champion, it's a 100% increase. You add that to a 200 damage champion, you only get a 25% increase. Mix attributes for the best effect.

Edit: There actually is one stat that is non-diminishing, that being Cooldown Reduction. If you had a nuke that did 1 damage per second and used 10% reduction for that, you'd deal 1 damage per .9 secs, or 1.11 damage per second. If you added 10% more reduction, you'd deal 1 damage per .8 seconds, or 1.25 damage per second. The first is an 11.11% increase in damage, the second a 12.5% increase in damage.