Let me tell a story....
I did some (very) minor design work about 5-10 years ago for a client who is older and not at all "tech savvy". It wasn't an expensive job... and really I only agreed to it because I was slow at the time. It was just a 3 page "brochure" static HTML site. Nothing real involved at all. And I went ahead an hosted it on a reseller account I happen to have. His site gets almost no traffic and the bulk of it's use is for email associated with his domain.
Since then, I've apparently become IT support for this client. Once or twice a year I get an (angry) phone call that he "can't get to my Squirrelmail". In fact, I got one such call last week. Although he's not angry at me specifically, his demeanor is just terribly unpleasant overall. He starts phone conversations (he doesn't like emailing) yelling, and I mean yelling at the top of his lungs with language full of expletives - just angry ranting. On more than one occasion I've had to calmly tell him "[Client], please stop yelling at me. I'm trying to help you but I don't like being yelled at. If you continue to yell at me I'm going to have to end this conversation." And then he does calm down. I do understand it's only out of frustration, but it's not something I should have to deal with.
My general feeling about the guy is he can go take a hike. I don't need to deal with people like that and I certainly don't care if I lose the $100 a year in hosting revenue from him. And on more than one occasion I've come close to just telling him he has 10 days to find new hosting and I'll send him files for his site. Knowing full well, this would put him in a complete tailspin since he doesn't understand ANYTHING about web dev at all. In fact, I've prevented him from being suckered in by scammers on multiple occasions offering to "improve his SEO" all they need is log in access to his hosting and domain.
However, this guy passes my name along to others. He's a millionaire and been in business for 50+ years. He's got a lot of contacts. And many of his contacts are older business owners who may be retired and no longer have a direct staff to call upon. So, he generates revenue for me in a round-about manner. So.... do I cut him loose and not get the occasional referral from him? Or do I deal with a couple hours a year as a loss leader for a better referrals later?
About 15 years ago I was negotiating with a prospective client. She lived in another state, but her and her husband wanted to take a trip to my area and meet me. I was hesitant at first. But after some conversation it was clear she just wanted a face to face meeting for a hour or two and that was it. The project being discussed was worth a few hundred dollars, but not really a lot to me, certainly not enough to warrant her trip. But I agreed.
She and her husband (both company owners) flew in, we had a pleasant lunch and they agreed to the project. That was the bulk of the meeting. They went home. They merely wanted to see my demeanor with them. They are immigrants and apparently often get treated as "dumb" by people merely due to their accents. They are both PhD holders in sciences and math. Far from dumb in any sense of the word. They merely don't alway speak clear English.
Since that time, this client has repeatedly returned to me for more work. Often with hefty returns for me. It was that initial meeting that she said made her feel comfortable working with me. In her words, "You didn't treat us as if we were stupid even though we can be difficult to understand at times." For much of 2000-2010 she was one of my leading revenue clients. Her business has been struggling since 2010, but I still get a couple projects a year from her, nothing that notable, but still stays in contact. Without that initial meeting I'm fairly certain I'd have missed out on tens of thousands of dollars in revenue over the years.
The point is... I, personally, never know which client is going to generate more revenue and more referrals than the other clients. So.... I treat them all relatively the same. I deal with the annoyance in return for good word of mouth.
If it were me, I'd meet the client if that's what they are requesting and it's not too much of an imposition on me. While a job for a couple hundred dollars may amount to nothing really, the word of mouth gained from it may be greater. But for $200, just the initial meeting.. not anything more after that.. email/phone should be sufficient afterwards.
Some people simply prefer to meet face to face to know who you are. It may have something to do with generational gaps, but regardless, some are just more comfortable paying people they can recognize in a crowd.