In the long term, if you one-box a heroic, you should receive 20% of the loot.
Sure you can be lucky or unlucky on any given roll.

As a boxer, we get 100% of the loot.
If you were to evenly distribute it, that would be 20% per toon.

An epic flyer costs 5000g (plus the mount) for one toon.
If one toon is gathering 5k, it takes so long.
If five toons are each gathering 5k, it will take just as long for a lot of content.
For example, the instance option will be the same, if you go with a group that has no ups there.
For example, with your guild on farming runs.
PuGs will rarely have no one getting an up from ToC normal, but boxing you can be sure everything will DE.
So with Pugs, a boxer has a gold advantage over a solo player.

Dailies earn gold for boxers faster then for solo players.
If you keep the gold earnt on each individual toon, they should have the same gold as one-boxing the dailies.
But boxers will kill things a lot faster.
And there are routes which are boxing friendly, so all mobs drop the item or its a kill quest.
In these cases, boxing is a slight advantage.
Also, dailies are boring; if you can only bring yourself to do them 2 days a week, the boxer gets 2.5k while the solo player gets 20% of that.

A boxer definitely has the option to save up on 5x toons, for 1 toon to purchase with.
For example, gearing your tank toon on the team, is the fastest way to be able to do heroics successfully.
A 1x boxer will gear the tank much more slowly, and be unable to do heroics for say 15 days of farming.
The 5x boxer will gear their tank in 3 days of farming.
And even though the other 4 toons are not geared, having the tank geared will allow all 5 to run heroics on day 4.

Farming is the one aspect which might favor the 1x boxer.
This is because of the limited number of resources.
If you can clear 75% of an area in the time it takes before respawns (I was doing this for Primal Fire in BC at Skald), you have 3/4's the resources on one toon per hour.
With five toons, you have 100% of the resources per hour, but each toon is only making 20% of that.
So, gearing all the toons off of farming revenue, is slower boxing then not.
But if you're farming purely for gold, it is still more total gold in the same time, just not as good an option for saving for something like Epic Flyers.