Why do some groups of tourists include someone carrying a banner?

For the same reason that Western and Near Eastern militaries have been carrying "colours, standards (and) guidons" for 7,000 years: so the troops know where the commander is.

https://en.wikipedia.org/wiki/Military_colours,_standards_and_guidons

In military organizations, the practice of carrying colours, standards or guidons, both to act as a rallying point for troops and to mark the location of the commander, is thought to have originated in Ancient Egypt some 5,000 years ago.

The ancient Chinese certainly had something similar, because flags are an obvious solution to the problem of letting troops in battle (and tourists in a crowded area) know where the leader is.

This is very common in China. You might have a number of tour groups simultaneously at a busy tourist site and the use of a flag (and stickers on the participants) helps keep them together and is very much necessary. Sometimes the tour leader will dress in minority costume as well (for example in Lijiang), which also helps them stand out from the crowd.

It's probably not as necessary in Thailand where it is unlikely a whole gaggle of similar groups will converge on one spot, but the participants probably feel more comfortable having the security of seeing the flag and having a travel company sticker.

Photo below (without arrows) from the SCMP.

Imagine maybe dozen tour groups, from many different tour companies, simultaneously at a single crowded site (say on a mountainside with a single spot where scenic photos of one or two people are preferred). Everyone is milling about and/or waiting their turn at the photo spot, buying food or souvenirs from the vendors, and it would be very easy to get separated from your tour group.

Chinese mass-market tours also tend to cram as many items as possible into their itinerary.

As others said, you'll see those everywhere, not only in Thailand. Each tour guide has a stick with some special identifying items, most often flag or stuffed animals, to make them visible in a crowded area. It's also useful for tours that tourists join individually and arrive at the meeting point on their own. European tourist companies more commonly use umbrellas, especially on free-walking tours.

I don't know why you said it's not unique but you don't usually see 2 guides with the same flag, even when they both use company flags and come from the same company because in that case they'll choose different ways to hang on the stick

In Vietnam and China you'll also see tourist companies giving each tourist a bright color hat so that the whole group can stay together, and one can find the group easily when they lost their way. It's also good for advertising the company