This works better the more intimate the setting is. I can totally see it working in a small town. Here's a handful of reasons this could go sideways:
Some bars are just slammed. Like, 40 feet of bar, entire front is 5 people deep squirming to get served by two people, and you have to literally scream at those people to get service. Ordering a $1.50 sprite in that environment is not only hellish for you, it's arguably a waste of the bartender and everyone else's time. There's a counterargument along the lines of "we all pay to be here, everyone's equal" but I wouldn't expect it to be a common take.
If you have a problem, yes, it's going to be extremely hard to resist.
Scarier still, you could be the victim of an innocent mistake. I don't eat dairy. My burgers come out with cheese on them by mistake maybe 10% of the time. When the kitchen's on autopilot, they absentmindedly make the default version of the thing, and there's no system to catch that mistake until it gets to me. That soda water becomes a gin soda really easily. If you just don't like alcohol, this is a trivial mistake. If you're in recovery, you are in serious danger.
But it's not that you can't resist. It's that you feel weird for resisting. I have a friend that didn't drink for many years. He got extraordinarily sick of having to explain himself. Even if the people you meet are 100% supportive, merely having the situation brought up can feel like a burden or like it singles you out. Many people find it hard to enjoy themselves in the shadow of this feeling.
If I don't want to drink, I take people to tea. You still have a pretense for sitting down in a strange dim room and having intimate conversation. Just without all the other bullshit. But I think an abundance of tea houses might require a fairly big city, at least in America.