There is no other reason to send heroes home besides for feathers or to keep the barracks from getting full. In fact, the most important reason to send heroes home is for feathers, which is the best way to collect feathers, aside from the Duel Arena.
In the arena, you can earn up to 7100 feathers per week. You're much more likely to earn between 1000 and 2000 feathers, though.
As you keep summoning heroes, you'll eventually end up with lots of 3-4 star heroes, which you might not want to keep if you've already decided on which heroes you want in your team. By sending them all home, you can earn between 750 and 1500 feathers per 20 Orbs (assuming you summon the full set of 5 heroes per summoning session).
You'll need all these feathers in order to improve the rarity of your heroes. A 3 star hero needs 2000 feathers to become 4 star, and a 4 star hero needs 20 000 feathers to reach 5 stars. Some heroes can not be summoned at 5 stars and therefore need to be improved using feathers.
1 and 2 star heroes aren't particularly useful, as they yield very little feathers and only provide about 10 SP when merged into other (3+ star) units.
They become somewhat more useful if you plan on keeping them in your team, as you can slowly improve them all the way to 5 star. Even if you already have the same hero with 5 star rarity, you might want to create another one for merging purposes. Merging two heroes of the same rarity not only provides SP, but also boosts the unit's stats without raising the unit's level.
However, that's only relevant in the endgame. And by then, you're much more likely to have found at least one or two 3 - 4 star heroes to use for merging instead.