Yes, sorry.
I thing it looks pretty much better if you see your weapon all the time, skyrim was also like that, but there you could use and addon.

It is like stealing a little bit of the epic game impressions, particularly when you play a tank

Agree , weapons and even the second weaponset shoould be visible to some extend.

For example wielding a 2H weapon (staff/bow/2 h melee) and you are using your second weapon set which consist of 1h+shield the 2h weapon should be holstered on the back.

Vice versa a sword should be sheated at the side and the shield should be on the back when the other weaponset is being worn.

Weapons visible while riding is a request to implement an even more immersed feeling.

adition to game mechanics:
Mount&Blade Warband introduced that you gain additional directional back armor when you put your shield on your back.

But then again M&B does have a weight system which slows you down, I do not recommend that in ESO because the fighting system is so different.

But it does look cool wielding something 2H and your shield is hanging on your back.

Whenever a game tries to render weapons on a mounted player it rarely works right in my experience, clipping and other graphics artifacts always make something look silly.

Would be cool to mount your weapons on your mount.

There's a simple fix for that. If you want your weapons to show while mounted, just stand on your horse instead of sitting. As depicted in following beta screenshot:

They did it because a lot of weapons / shields would just go through the horse and that would be tremendously ugly. I wish they would hang them on the side or something of the sort.

A grand mmo managed to implement this 9 years ago.