To me functioning well and terrible do not work together.
When I say her kit functions well, I mean that its design is perfectly fine, and numerically it doesn't work because her numbers just aren't high enough. The damage is too low, the mana costs are too high, etc. That doesn't mean the kit's design is screwed. For example, say I took Leblanc and just cut her damage in half, or cut her health in half, or doubled her cooldowns, or something else like that. The kit would be fine and perfectly functional, but she would suck because she was numerically underpowered. This is what Taliyah is like. Her kit works fine with itself and would allow her to do her job without being oppressive if her numbers didn't suck.
It's so easy to go in for a gank with taliyah and feel like you accomplished nothing at all,
Of course. It's easy to do anything as Taliyah and feel like you accomplished nothing. She's weak! Accomplishing nothing is the baseline!
I can think of quite a few ganks I've had with her where if I had more damage or could have gone in from a longer range, there would have been a very different outcome. That speaks to me about how much her general weakness is affecting her ability to do her job.
The fact that she is objectively weaker in the zones she creates means she wants to be out of those zones as much as much as possible. This to me feels completely counter intuitive to what a control mage is trying to do, and the mechanic really lends itself to a more kite centric play style.
"Control mage" and "kiting" go together heavily in my mind. When I'm thinking of someone like Orianna, Karma, maybe Syndra, I can't avoid thinking about how they all move around a ton. It's pretty characteristic of their gameplay. I don't find worked ground tends to be a significant limitation past the laning phase because I don't want to be standing in the same pieces of ground anyway. I may want to be in the same general map area, but worked ground allows that. I've never found my role being limited when I play taliyah because of worked ground. I can always, without exception, stay where my team is and fight with them once the laning phase is over, and as far as I'm concerned that means
What would you change about her current kit to make her not terrible? Just numbers?
Numbers primarily. Lower mana costs, lower ult cd, possibly a higher ult range at lower levels, increased damage. Those are the main components. None represent significant changes to her playstyle. I could be swayed by an argument that worked ground should have a shorter duration to make her laning phase easier, but aside from that, I can't think of any mechanical changes that stand out as a necessity.
If the zones just slowed enemies
I don't like that idea. Having a constant slow in such a large area is going to necessitate that either the slow is so small that it doesn't matter, or that it is going to make immobile champions completely unable to deal with her because they can't deal with an infinite duration slow.
In addition I don't even think it would feel good to play with. First, I don't want to set these up before a fight. Nothing else in her kit has any kind of setup element in it, and it goes against the engage potential her ult promises. Additionally, I think it has problems with being uninteresting to actually use. She already fulfills a kiting control style between the slow on her E and the constant slow from her Q with Rylai's, so this would be a mechanic that wouldn't actually impact the enemy she's directly engaging. It wouldn't syngergize with her kit and her build because she already has this effect against enemies she is directly fighting. If a significant portion of her power gets tied into slowing enemies that she isn't actually targeting, then that is power that isn't going to be enjoyable for her because it's going to be much less noticeable and she isn't doing anything to activate.
Something as passive as that doesn't feel like something that should be on her kit. I don't think them having a negative effect on enemies is a good idea in general. If worked ground is a problem, then we should either reduce its effect on her by decreasing the size/duration, or increasing the benefits it brings by tooling up the movespeed or adding something else she'd like to it.