So there are a few things that make her, not necessarily a bad choice, but a mediocre one mid. Take these reasons with a grain of salt, as I am neither great at league nor have I played Zyra mid in quite a while.
Zyra tends to push the wave with her abilities. with more gank paths to ward and no mobility, shoving the wave in leaves her susceptible to ganks. When her plant targets off an enemy vhampion, it hits minions in range for the remainder of its life span. with the addition of random seed spawns, it's really hard to hit a champion without proccing a plant in range of the minion wave, and there's no way to stop them autoing minions. As such, her only way of escaping a gank is to save her e, which roots for a total of 0.75 seconds at rank 1. You either rank it up first, which means giving up on damage and still leaving yourself vulnerable when you clear a wave or trade with it, or you leave it at rank one and need to commit a melee plant to it to get it to properly dissuade the jungler. This not factoring in that it is slow enough to dodge at the edge of its cast range, so it's not quite a guaranteed cc ala Syndra stun.
Her wave clear is rather slow compared to most immobile mages, with a fair bit of her damage back-loaded onto her plants. as such, she needs to stay forward longer than her fellow mages to clear a wave. Meanwhile, mages with similar mobility issues tend to have higher ranges and/or clear the wave much faster. Viktor, Velkoz, Lux, Xerath, even some more mobile mages like Ziggs and Ahri, have the ability to clear casters with a single cast. This of course keeps her gankable for longer periods of times, as well as giving the enemy laner more time to punish her if she's behind, or force her off the wave and pray her plants get her the cs she needs.
Her base stats are some of the lowest in the game; mid laners with less health include Anivia, Lux, Veigar, and Heimer. Of those, all of them end up with significantly higher armour. Lux significantly out-ranges Zyra and has a shield for additional survivability. Anivia is given lower health to both weaken her early game and because of her passive. Veigar struggles early due to his scaling, but even he can clear casters fairly early with w, and is incentivized to use his fairly long range q on farming. Heimer... I don't know enough about this champ to explain why he's so squishy lol. Is he even a mid laner anymore?
In addition, Zyra has pretty abysmal armour, and it scales poorly too, to an eventual 71. As far as mid laners go, the only mid laner with less armour than her are Orianna (minus passive resists from having the ball on her) And Azir (again with the range thing, but I guess theres a rework to change that, so I'll reserve judgement.) So she has a hell of a time against anyone with burst (ie: most of the mid lane roster) and has a particularly hard time against ad mids.
She has 2 damaging spells that provide her a ratio of 1.1AP, 1.8 with ult. These ratios are decidedly lackluster for the purposes of quick damage compared to similar mid laners. This is, of course, balanced around her plants, which add 0.15AP ratio per attack at an AS of 0.8, with plants after the first dealing reduced ratio equivalent to 0.075AP. The reason her ratios are kept comparatively low are twofold; she has pretty significant base damages to make her plants deal relevant damage in the early game, and her low burst is tempered by a significant potential for sustained damage with her plants, particularly with her ult's passive effect of increasing plant dmg. Without Ult, a plant at lvl 1 has a potential ratio of 0.6 over 5 seconds. The duratio goes up to 7.5 by lvl 16, giving a potential ratio of 0.9, with additional plants on the same target giving her an additional 0.3-0.45AP per additional plant. Her ult gives her plants an effective increase of 50%, bringing that up to a potential 1.35+0.675 per additional plant on a target over 7.5 seconds. So a significant portion of her AP ratio is backloaded into her plants, which tend to survive their full duration in the heat of a teamfight, unless they eat multiple aoe spells, due to their unique health mechanic. Not even covering her base damages, this is a hefty load of damage. Unfortunately for her, you'll never get anywhere near this much damage against a halfway competent opponent in a 1 on 1 (halfway competent including more of the population of silver than not.) So, her 1v1 laning suffers as a result. In the 2v2, things tend to get a little more hectic, allowing the plants to do more in the all in or extended trade. Her poke, by contrast, is met or beaten by similar mage supports (Brand, Sona in terms of her poke potential, Lux sort of, Annie once upon a time... there really aren't many mage supports these days, huh? If I'm missing any obvious ones, lemme know.)
Then of course is the factoid you hear all the time: Zyra has really high base damage. Lets look at how much AP you need to double your damage on her abilities, at max rank, shall we?
Q- 333.33 AP
E- 400 AP
R- 500 AP
Plant- 760 AP
I would argue that her base to scaling damage ratios are roughly in line with other mid laners on her q, e, and ult. The AP ratio on E is definitely on the low side, but that's not unusual for a hard cc ability. The really standout number there is her plants, which seem to be pretty significantly skewed towards base damage. The reason you hear about how Zyra's ratios favour base damage over scaling seems to be coming almost entirely from her plants. This is probably not entirely without merit, given how much of her damage is on said plants. In laning phase, when the abilities are doing more work than the plants, the ratios are a significant part of the damage. As the fights get bigger and plants take over, she oddly enough relies more and more on her base damage. This might explain why she looks at going on hit and utility items later in the game, with some pen to amplify her already existing ap damage.
Based on these reasons, I understand why she is seeing more play as a support, and struggle to see a solution that renders her effective in the midlane without draining that effectiveness from her support ability. If I were deadset on seeing her moved back to mid lane, I would suggest exploring some of the following avenues:
- Increase the bases and reduce ratios on her base abilities, and vice versa on her plants. This would allow her to use the more effective early game tools in her kit to trade in lane, and would force her to build AP to still retain her strong damage in late game teamfights via plants.
- Increase her base health and possibly armour. This would allow Zyra to better survive the laning phase against her lane opponent. To counterbalance these changes for her support playstyle, you'd look at a reduction in base damage on plants, which see minimal use in mid lane trades. They could probably scale up to more or less the same, they'd just need to be brought in line for laning phase.
- Increase ability damage to minions. Pretty sure this is not the change she needs, as it further reduces interactivity in lane, but it would allow her to run up, clear the casters, and leave, mitigating the effect of bullying and allowing her to stay safer in lane.
- Perhaps increase the root duration on e rank 1, allowing her to better survive ganks? To make that not broken on support, you'd need to tweak damages, but that'd probably hurt mid as much or more, so not sure on this one. Might be a lever to toy with, anyways.
- Reduce plant duration, and up the damage per attack, for the same total damage just dealt over fewer seconds. This is probably a change you make in tandem with other ones, but basically it will reduce the window over which she deals her burst damage. This unfortunately reduces the enemy's ability to dodge plant damage by walking away form it, as half the plant's potential damage probably gets applied to someone even if they just straight run from it. Maybe this would be balanced by the fact that she can't zone quite so hard, or provide as much vision, but... worth checking.
Anyways, that's my two cents, lol.