Again I'm not seeing how you come to this conclusion based on the evidence.
Hmm, I'm not the best at explaining such things, but I can try:
Read this carefully, if you haven't.
Greataxe > Maul if 6.5t > 4.5n, which is likely but marginal.
Greataxe > Greatsword if 5.5n + 6.5t > B, which almost certainly true.
Maul > Greatsword if 10n > B, which is very likely.
This is purely from a damage perspective, over 20 attacks. So, let's looking at characters at 3rd, 9th, 13th, and 19th for a moment.
3rd: +4 Str, +1 Feat, +1 Enh. B=6, 2 Encounter powers for 2W over say 2 encounters, 1 Daily for 3W, n = (3+2*2*2+15)/20 = 1.3
Greataxe is .65 > Maul which is 7 > Greatsword, over 20 attacks or .03 per hit better for Greataxe over Maul and .35 per hit better for Maul over Greatsword
9th: +5 Str, +1 Feat, +3 Enh. B=9, 3 Enc for 2W over 2 encounters, 2 Daily for 3W, n = (3*2+2*3*2+12)/20 = 1.5
Maul is .25 > Greataxe which is 5.75 > Greatsword, over 20 attacks or .01 per hit better for Maul over Greataxe and .29 per hit better for Greataxe over Greatsword
13th: +5 Str, +2 Feat, +3 Enh. B=10, 4 Enc for 2W over 2 encounters, 2 Daily for 3W, n = (3*2+2*4*2+10)/20 = 1.6
Greataxe is 5.8 > Maul which is 6 > Greatsword, over 20 attacks or .29 per hit better for Greataxe over Maul and .3 per hit better for Maul over Greatsword
19th: +6 Str, +2 Feat, +5 Enh. B=13, 4 Enc for 2.5W over 2 encounters, 2 Daily for 3W, n = (3*2+2.5*4*2+10)/20 = 1.8
Greataxe is 4.9 > Maul which is 5 > Greatsword, over 20 attacks or .25 per hit better for Greataxe over Maul and .25 per hit better for Maul over Greatsword
So, no matter what the damage difference is fairly negligible. Meanwhilst, the greatsword holds an advantage whenever
1) You're attacking a minion
2) You're attacking someone low enough on health
3) You care about the on hit effect of your power
So, if you had to look at it in feat or feature form, would you prefer?
1) You deal .4 damage more per attack
2) You kill 2% more enemies (20% of foes, 10% of the time) and you hit with special effects 10% more often (ie, 11 hits instead of 10)
At a minimum, that's clearly a viable choice.
If you make the greatsword d12, then it's just a landslide win as it will both deal more damage, kill more enemies, and land special effects more often.
Let's look at a 3rd level paladin for a moment and see what powers he's likely to have, for whether he might care about hitting versus hitting harder when he does...
At-Wills: Bolstering Strike and Enfeebling Strike
Enc 1, 3: Fearsome Smite and Righteous Smite
Daily would use an implement, so can ignore for now.
So, 10% more temp hp gained over the 20 attacks, 10% more often giving the enemy -2 attack
All in all, works out to 7.65 less damage dealt, 10% more minions killed, 5 more temp hp and 20% less of one attack - call that another point or two of damage intercepted.
Certainly seems viable enough to me. A fraction less damage per hit for better at doing their job. That's a real choice and unless I was building such a character explicitly for backup damage, I'd almost always side with being better at the rest of the job.
Err... falchion is high crit. So on a crit, it does an absolute minium of 10, not 8, and can beat the GS by up to 6 points.
Sure, but the .5 damage per W on normal hits you get from the greatsword is a benefit too, so the extra 2d4 * t - (2 * W) that comes when either crits doesn't automatically boost the falchion ahead... and the falchion suffers on multiple W attacks as well.
Of course, that all then falls apart at paragon and epic where the falchion is just far and away the superior choice.
The falchion is a poor choice at heroic, an equitable choice at paragon, and slightly better at epic.