If you ever had AmEx (I do) you already know that, a lot of places in US and more in Europe do not accept AmEx. When I go to some place I don't know I usually take AmEx, Visa and Mastercard - one of each. It can be very useful in all kinds of weird situations - like when I had some ticketing machine in Europe that was sure every Visa has a chip and a PIN code (American ones of course do not) - but it gladly accepted AmEx without any codes. So variety helps :)
So, I'd say it indeed may be a good idea to have a Visa card - along with their competitor's cards.