Why is Shen so weak?

I've been playing Shen for a while now and I keep think that he is very useless tank. Here are my opinions,

1. Shen does not do enough damage to scare people in teammate but if I build damage, he becomes very squish bruiser.

2. His ult late game is almost useless as the shield is just only two shots for adcs to remove. And also the ult itself scales with AP which no one builds Shen AP so there is no way to make your ult more powerful.

3. His only cc which is Shadow Dash is very easy to dodge and if you miss it, you're just a walking tank with no gap closer. (Also your Dash itself uses like half of the energy which is insane amount).

4. His split pushing ability is actually very crappy. Even if you have items like Sunfire Cape and Titanic Hydra, your split pushing speed is very slow compare to other champions (ex. Jax, Yi, Nasus etc.). And you are very slow at taking down turrets.

5. If your team is behind, it's really hard to come back because Shen's abilities don't really provide much help (see above)

Now these are just my opinions about Shen but I think there is a pretty good reason why people don't play Shen frequently.

So my actual question is, am I just bad as Shen? or is Shen just useless?

(If you guys think i'm a bad Shen player, please give me some tips on how to improve my Shen.)