It's about the same as looking a homeless man right in the eyes as you drive off in your Benz without giving him anything.
It's totally doable, expected even, people do it all the time. But anyone with a functioning moral code probably feels a bit shitty about it, even if the circumstances around the source of the problem are largely out of their control.
The No Tip button says "I'm fine paying money to your corporate overlord but not to you, specifically, peon." You're specifically opting out of the ability to directly benefit the workers of a company rather than the management.
The discussion around why tips are an expected or "required" part of this transaction is another story. But so long as food service workers are being paid $2.13 an hour plus tips I'm going to continue to tip the guy that makes my tacos, largely because I feel that's probably the only semi-ethical way for me to excuse buying those tacos.
And before you say "if they don't make enough in tips to equal minimum wage then the employer pays the difference", that is true, but you should also know that it is true that those people do not retain employment.