Why is Diana's Playrate so low?

She's probably just not that interesting. I mean hell most of her gameplay to me was fishing for Q's then clicking on them afterwards. Low playrate can be a result of players finding the champion not fun, it could be because the meta doesn't favor them or the champion is just weak but I doubt it's the latter.

melee assassins with no option to escape fights just aren't popular in general

She's boring, to be completely honest. You get tired of her so quickly.

shes too simple, and her kill zone isn't 100-0, she needs a little bit before hand to put them into kill range or to go after a target with 0 mr, and its extremley common to build 1/2 mr items and then shes forever out of your kill range, but shes reliant on going in to do her damage, but if she never goes in she does nothing at all, and if the enemy team can survive the burst then you dont want diana to just die afterwards.

shes just a 5/10 champ, not the best at anything but not awful enough to buff.

She has no escape unlike other assassins

Idk if you've noticed, but the more faceroll things seem, the more people play them.

Diana can't faceroll from level 1 and do stuff.

Ryze can just mash Q and E on a minion wave from level and feel like he's doing big stuff, although this is why he has such a low winrate...some people don't realize that it takes more than that to be successful on him.

Because she sucks in most lane matchups and is useless from the JG till 6. That's very bad in this meta.

She's not a bad champion, the current meta just does not give her opportunity to flourish is all. She can still be pocket picked under the right circumstances.

She doesn't have a kit that is functional until level 6 like kassadin.

She can be quite oppressive in low elo since the most MR you'll see in any given game is maybe a spirit visage. I think most people see her Q and find it daunting even though it's one of the easiest skill shots to land.

Diana's kit is just weird. Well, to me it's weird. Literally, I've played her for about a year now on and off, you mention ryze in your comment also, I play ryze for a year I get an 83% win rate nowerdays in ranked, I play Diana and I still can't decide whether shes fit for mid or jungle. I play her jungle but she wastes SO MUCH MANA. Like you do 1 rotation and your basically out of mana, that's the biggest issue I've had with her. Her kit for me just doesn't fit this meta, it requires jumping in but your a squishy target so you just get bursted by assasins easily. Also, ryze's win rate is merely due to players who are inexpreinced with him, as a ryze main I find him busted and elegant to play, but for a new player hes a 450 champ and his skill curve is pretty huge as far as I've seen