Why do so many enjoy archery?
1) You can do damage to enemies before they can harm you. From sneak and while enemies "close the gap."
2) Easier to take out high priority targets w/ ranged sneak
3) Poisoned arrows, poisoned arrows, poisoned arrows. Add dam or debuff your choice. The synergy between alchemy and archery is amazing. Being able to do this from the safety of long range and not in melee range is what makes this ability shine.
4) You're not getting a sneak attack bonus with ranged magic.
5) You don't wait for dragons to land. You force them to with an arrow to that soft underbelly.
6) Bows are silent and don't break sneak.
7) Harvesting souls with a soul trapping bow is quite effective since you have the ability to one shot most low lvl monsters from sneak.
8) Arrows have no weight.
9) Making insanely long distance attacks and other impossible shots for style points.

10) Stagger perk makes bows completely viable in CQC. Smashing enemies in the face with your bow is also entertaining.
11) Adds something to any build that lacks ranged combat. Warrior archer, mystic archer, etc.
12) The paralyze ability from enchantments and perking makes you a ranged damage crowd controlling god.
13) Only need 3 perks from the sneak tree for max synergy w/ sneak.
The problem with archery? It is too damn good.