It isn’t literally doing nothing, but it accomplishes absolutely nothing tangible. Plus it insults people like me that don’t want your prayers. I don’t think you should make your decisions based on what assholes like me want, or what anyone else wants for that matter, but if your goal is compassion then you could consider how your offering of prayer might be the equivalent of the middle finger to some.
I think very few would consider it the equivalent of the middle finger, even if they did I would still pray for them. What I would not do is use it as an excuse to do nothing to solve the problem.