yo i'm (kind of) a zyra enthusiast (she was my 5th most played champ last season w/ 72 games) and while I agree that her kit has some huge flaws that stop her from being worth picking in a competitive environment, such as zero mobility and next to zero utility when behind (at least when compared to picks like janna and alistar that are still guaranteed to put in work even if feeding), she's still perfectly fine as a solo q stomper.
for starters, frost queen's claim (even with the 6.2 nerfs) is stronger than it ever was last season, and that's an item zyra benefits from like crazy for obvious reasons (and also because her core build is expensive like hell in comparison to other support picks that usually only need boots + sightstone and maybe fqc to put in work).
also (i could be wrong here though), her bot lane match ups against common supports are looking quite neat right now. it's true that you get blown up by shit like lucian/graves, but who doesn't. zyra's strength from an utility standpoint is the ability to zone adcs when their supports go for an all in (which should happen a lot with poppy/alistar's popularity), using her root + w combo and ultimate if it's available. against weaker lanes that have no all in potential you can just poke dudes with q+w and some auto attacks in between (note: DON'T TRY THIS AGAINST SORAKA LOL). a cool zyra mechanic that every aspiring zyra player should practice (tfw no sandbag) is using her plants to block crucial skillshots such as ez's q or thresh's grab, as that really helps snowballing lanes (imagine a thresh going for a lvl2 all in and blowing his most important cooldown on a plant. you can proceed to snowball the lane w/ the 10 sec window that gives you). anyway, the coolest part of support zyra is that she fucking hurts after she gets fqc + haunting guise and if she ever gets to 2/3 completed damage items it's nearly impossible to lose. just drop an ult between the opposing backline/frontline along with some plants, i swear to god solo q players (even in diamond+) just suck at teamfighting against a zyra that doesn't fall behind.
re: zyra vs morg: if you're not confident in dodging her q run MS quints. max your own q until level 6 and poke her with that + plants while dodging her skillshot. if she saves her spellshield for your root it won't be as bad because that's not your main method of winning the lane, but if she blows spellshield in a dumb way feel free to drop an offensive root if you know the enemy jungler isn't near (note: offensive roots usually suck. it's too slow for that, so you usually just use as counter engage/disengage tool)
note: i'm kinda ignoring the fact that some adcs are beyond retarded right now because that also benefits zyra. both graves and lucian are probably nasty w/ zyra, and ezreal is easy to beat if you're competent due to the way his damage works (just don't be a retard and stay in bush to eat some skillshots unless you're confident in your plant mechanics). also, idk what to expect of zyra's rework. they'll probably make plants less oppressive unless they're used in tandem with her ult while giving her a fancy tool. for example, a neat new passive would be bonus movement speed while walking towards her plants