It's mostly a matter of what she really brings.
As a support she has her shield. MS boost/slow. Limited hard CC(by limited I mean it can be avoided). Vision.
All of this is comes at a high cost in mana. Often requiring her to repeatedly use her Q. If her Q is out, she has to use Q or E for her W. Making her abilities all come with a delay.
Her overall range isn't long enough to be considered a poke support.
Her damage/burst isn't strong enough to be considered a kill lane like Annie.
Her CC isn't fully reliable, although very strong.
As a support, not having strong mana regen is very punishing.
Nami out classes her in almost every way in this area.
W's range is actually fairly strong if you cast it on yourself or an ally first. Q's range isn't too bad either.
QWREx3 does a fairly strong amount of damage. Nothing TOO impressive early game. She's not a kill lane either, but she'll get you kills easier without needing an ult.
CC does have a delay to it, but Q can be used much more often and R is fairly easy to hit.
Her mana can be a pain, but it is manageable with decent regen.
So why isn't Nami played mid? Because with items(regen+cdr) Orianna becomes a powerful utility mage. Nami doesn't become nearly as powerful. This is mainly because of Orainna's mana costs to keep using her abilities. Getting to a point of mananing that easily makes her a powerhouse. There's a reason she's top 5 in URF.