I disagree on three counts.
First, I don't think very many people are "falling for" it at all. I think for most people, it's a pose they adopt for personal amusement, or as a result of some other dissatisfaction already present in their lives. I think very few people are actually believing the Earth is flat.
Second, so what if people believe the Earth is flat? For almost everybody, almost all the time, the Earth *is* flat, in every practical way. Even the parts of your daily life that really do depend on the Earth being round, like GPS on your phone, work whether you believe them or not. About the only people for whom the nonsense of a flat Earth needs to be exposed are space mission planners, and they already know the truth anyway. As nonsense goes, the flat earth is a good example of nonsense that doesn't really need to be exposed at all.
Third, it's trivial to expose, for anyone who actually wants to have their mind changed. But flat-earthers don't want their minds changed. You're trying to solve a problem of information, but the real problem is one of choice. You're talking about it as though we have to expose a great lie for the good of all mankind. But I think you're actually just trying to put a stop to a game of silly buggers that you don't approve of. Let it go, is my advice. It's not actually all that important, and the people you're trying to stop from having fun aren't interested in quitting their game on your account anyway.