Refusing to tip as an individual kinda shows a distinct lack of understanding of the issue and a lack of interpersonal skills.
First off, I would hazard a guess that most Americans don't particularly like the tip system. They just understand that refusing to tip only hurts the individual service person. Basically a restaurant owner is unlikely to change policy within their establishment because people don't tip, they're not directly affected by their wait staff losing money.
Your approach also shows a lack of a rather important interpersonal skill, empathy. Effectively you're saying that you don't care that you're hurting, what are already, low wage workers. You're fine with having a negative impact on the quality of the life for these workers just so that it doesn't come out of your pocket...
If fighting the tip system is really important to you, boycott the businesses, don't just withhold tips. Both approaches hurt the workers, but at least in this way you're also putting a little pressure on the business owners.
Or if you really want to see real actual change, encourage and support labor unions. That's where most of these kinds of large systemic changes for workers come from in the United States. Collective bargaining, through unions, allows workers to stand united and demand a living wage.
Taking a step back and looking at why a culture does something is an important step before attempting to change what a culture does. Probably one of the the major criticisms of American culture is that we have a history of not bothering to understand a culture before trying to change it.
The idea of "American exceptionalism", the idea that our way is inherently better, has caused an awful lot of problems throughout history...
Probably best to learn from our example, lest you end up with our reputation.