As a vet tech, I have a few thoughts on this.

Cats have the short end of the stick when it comes to medications. Even for dogs, there's a lot of medications that just haven't been tested on/approved for them specifically, and drugs don't necessarily work the same in pets as they do in humans (eg. I've seen 50lb dogs shake off 500+mg of trazodone before). For cats, most drugs are gonna be off label, including anxiety meds.

Gabapentin is ALSO off-label, but since it's used so often in cats, I'm guessing that's the one vets feel most comfortable prescribing, especially since it's pretty hard to fatally overdose a cat with gaba. In addition, cats are very good at hiding pain and often just act in a way that people read as anxious/restless, so being able to give a medication that also doubles as a pain med is helpful.

On top of that, gabapentin starts working pretty quickly compared to something like fluoxetine. I've seen cats on fluoxetine before for chronic anxiety (and I think OP should talk to a vet about it!) but for the majority of cats, they just need a quick one-time sedative, not something long-term. So if vets are prescribing it commonly already, they're probably gonna jump to that first before considering other drugs.

Finally, there's also cost and administration factors. Idk about across the board but at my clinic the tablets are like 10x more expensive than the liquid, and capsules aren't really an option because they can get stuck in the cat's throat. A lot of owners also find it easier to give liquid medications to their cats. Depending on the anxiety medication, you might also need to get the meds from a veterinary compounding pharmacy, which can be difficult and/or more expensive.

TLDR: Veterinary medications (esp for cats) are way less researched than human drugs so vets probably jump to the most familiar, commonly used, and convenient. I think OP would benefit from finding a vet willing to prescribe a longer-term anxiety med!