Martin Luther King Jr. was arrested many times, and he was a strong advocate and practician of peaceful protesting. Sometimes even peaceful protests result in arrests. The reason that no one was arrested at the Women's March was not that it was a peaceful protest. Certain groups are allowed to protest peacefully, and others are not.
No, peaceful protesting is not the most efficient way to resolve political issues. It is, however, a very good way to start the process. When people assemble peacefully to draw attention to an issue that they feel strongly about, especially when they gather in such large numbers as for the Women's March, it sends a strong message to those in power that the people see problems that need to be addressed. While this is a good thing, it's just one step in what can be a long process to bring about change. After the marching, the protesters need to continue pressing their elected officials to make needed changes.
Peaceful protesting is a great way to make your voice heard. In large numbers, it draws attention to issues and can even get the attention of the media. But the real way to make your voice heard is to vote. You can make sure that your candidate has a chance of winning office.
So-called peaceful protests does little to motivate change. All of the government programs that were championed by the women's march require money to operate. This money comes in the form of tax revenue. Therefore, if people support these programs, they need to contribute more in taxes so that the government can afford to fund them.