Confused about the smithing tree...

So obviously left side is for light armor, and right is for heavy armor

Say I play an Archer, and I'm wearing and improving light armor... I can't improve a daedric bow unless I go right side on the tree as well
correct? this seems counter-intuitive and kind of a waste of perks right??
maybe I'm missing something here

Also say I get named armor like nightingale, can I improve that even though it isn't listed on the tree - if so what perks would I need?

Thanks alll

You can improve special gear.

Depends on the gear I think. I upgraded the Dark Brotherhood armor and it was Leather.

you can imrpove it but there is no perk that makes the improving of nightengale armor better..

You can improve any BASIC weapon or armor, no matter the skill level or perks. If you have a Smithing skill if 100, all you need is to increase that by 68 to improve anything to Legendary status. This can be done by combining potions and or wearing enchanted gear, OR by selecting the app perk for that type. Perks basically translate to 68 increase in skill level.

I only forego two perks, to get Arcane Blacky. That way you can improve enchanted items. Some special items cannot be improved at all and some only improved to Flawless status. The effects of perks, potions and enchantments will stack to get them to legendary, as well as make some truly powerful, and arguably overpowered items. Use with caution.

You can always improve anything. The perks just make you able to improve them even more.