If low-level PCs can take roughly three hits from level-appropriate enemies, and high-level PCs can take six, is this a good thing or a bad thing? Do we want the ratio to remain constant? Or do we need relative damage to decline, because we want to give high-level characters more attacks per round?You have this today. A low level foe tends to hit for 1/3rd of a low PC's hit points.
The difference is that high level foes in 4E tend to hit for 1/6th of a high PC's hit points and DMs have to go out of their way to create monster groups that have good synergy and many attacks per round to overcome this. Course, they rarely can due to the vast plethora of temporary hit points, resistance, surgeless healing, and normal healing at high levels. The PCs have too many ways to reduce this damage even more.
The reason your claim here is inaccurate is that damage in this type of model is significantly decreased over what 4E does today. It's ratio-ed out to an appropriate level. It's not just +1 more damage per monster level.
How do we want to control the ratio? If we keep damage and hit points static, the ratio stays static. D&D has historically ramped up the hit points tremendously, and only recently has it ramped up damage, too.
It sounds like you'd like to keep damage and hit points strictly proportional, presumably with no increase in number of attacks per round?That's one of the flaws of 4E. It's sweet spot changes. This type of model avoids that.
Again, we can do that by keeping damage and hit points static or by increasing them at the same rate.
If you want a Fighter wearing heavy armor to be just twice as tough as a Wizard, that suggests no difference in hit points or armor class from character class or abilities and only a tiny difference in armor class from heavy armor.Personally, I think that PCs should hit same level foes about 60% of the time and that it should take 3 to 4 hits to take out the foe (almost regardless of class except for Strikers). I think monsters should hit PCs 40% (vs. melee class) to 60% (vs. non-melee class) of the time and that it should take 3 hits to take out a non-melee class and 4 hits to take out a melee class. In other words, 10 attacks (sometime via multiple attackers) to take out a melee PC and 5 attacks to take out a non-melee PC (by this, I basically mean a Fighter vs. a Wizard, there is room for shades of gray in between).
It also suggests that a Fighter shouldn't be able to take on three Wizards in hand-to-hand combat with no spells involved.