Why is there no Weapon skill Ultimates ?

Maybe hitting something with your weapon isnt awesome or epic enough to be classified as ultimate.

Why are we forced to use Magika dependant Ultimates only?

You arent, ultimates are not based on magicka or stamina, they're seperate abilities based on... ultimate.

If you're really wanting an ultimate ability that comes from a stamina-only tree, use dawnbreaker from the fighter's guild skill line.

I can think of three reasons:
I. To make room for more active skills.
II. Its hard to conceptualize.
III. Balancing acts.

The second point is the big one from a lore perspective. Ultimates are always big things that no mortal would usually be able to do with any regularity, like summoning a powerful atronach when they normally have little familiars or covering ones self in liquid steel to become just short of impervious. This is hard to adhere to when Elders Scrolls warriors are more grounded.

Point three is big too. If weapon lines had ultimates, they would have to scale off of magicka/stamina as well as weapon damage (all ultimates currently use spell damage). This means that equipment and spells can now boost your ultimate to absurd levels. Take Flawless Dawnbreaker for example. At high levels, the soft caps for spell damage is about 87, and the soft cap for stamina is about 2015; this leads to about 589 damage per use, which is pretty respectable. Now if we switch that to weapon damage, with a soft cap of about 189, we now have dawnbreaker hitting for 901. The weapon softcap is also really easy to surpass; a VR10 legendary two hander does about 160 damage, and damage buffs like momentum and surge with send that through the roof. This would make balancing a nightmare, and would make gear dependency even more of an issue than it is already.

But you are right, there currently aren't enough stamina-based ultimates