My wife hasn’t ever had anyone with that reaction, but that might be because of the venue: she sells at art fairs, where all the vendors are individuals. If a customer was leery about sharing credit card info, he/she would probably plan on paying with cash, anyway, and not even consider offering a credit card.
One nice thing about the Square, specifically, is that there are no up-front costs, no monthly costs, and almost zero effort involved in setting up an account and using the app. That’s ideal for someone like my wife, who’s a sporadic user with relatively low $/year sales.
It also might be good for someone like you who’s unsure of the relative utility of competing companies, because you can abandon it and move to another service without really losing anything. However, if you’re selling enough that you’d consider buying a stand-alone machine, you could probably do better by comparing different plans, as **jacobsta811 **says.