After reading through the thread I fail to fully understand arguments for Arthur being being better than Shanan
First of all Shanans stats are quite good plus he starts with a considerable level advantage, so Shanan w/o Balmung > Arthur w/o Holsety by a long shot
Second Arthur going into Wrath range is not exactly a good thing, that necessitates that he has lost 50% of his HP and therefore if anything you should get him out of Wrath range soon before he dies. You cannot say that Wrath compensates for offense issues with Arthur because it is rarely a good idea to walk around at <50% hp, that only works for special situations like one shotting Ishtar
Third, when there are many ranged enemies, one would usually think that you do not solo them with Arthur (although that is possible with Holsety, it would be expensive) nor with Shanan (since it would take too long), but rather you throw your own army at them and since both Shanan w/ Balmung and Arthur w/ Holsety are unlikely to be attacked on the enemy phase, the difference in range between them is of minimal importance. However if the holy weapons are not in play then you must be much more careful with Arthur's positioning since he is defensively more vulnerable compared to Shanan
Fourth, Arthur doesn't get a horse until he hits 20, and you can take more liberties with letting Shanan use his full move each turn, since he is again stronger defensively than Arthur (unless holy weapons are in play once again, but you cannot use Holsety 100% of the time from the very first chapter without money issues). Also, FE4 is not a race, there are no chapters where you are under time pressure, therefore it is entirely reasonable to take your time moving your full army around. Finally, the number of mounted units in the 2nd generation is not as high as their number in the first generation, therefore if you rush around with your mounted troops and leave foot soldiers like Shanan behind, you will not have enough people with you to fight enemy armies; therefore, having a mount is not as big of a deal since you will have to wait for the slower moving people anyway
So I say that Shanan w/o Balmung > Arthur w/o Holsety, and there are situations where Shanan w/o Balmung can bail you out, Arthur w/o Holsety cannot, and there are no immediately obvious characters who can do the same thing; and that Arthur w/ Holsety > Shanan w/ Balmung, but all situations that can be handled with Arthur w/ Holsety can also be handled by Shanan w/ Balmung, at the cost of some time and turns which is not of significance in FE4, or overall
Shanan can do anything Arthur can do, with or without holy weapons.