This is just my opinion and I can only speak from a US perspective, but yes and no. The ones who are able to do this have already gotten a 10+ year head start and have built up a deep network from which to source work from. The ones who are starting out today are more than likely having a very tough go at it. Competition for contracts is much more intense compared to 10, 15 years ago and you really need to bring more to the table than just "javascript developer" or "wordpress consultant".
I know there exists this love-affair on HN with running off to become independent contractor, live on a beach writing code and making your own hours. I'm not saying it's impossible, but the reality though is that in the end you are building a business (even if it's just you). All the energy, time, risk and money that it takes to run a regular businesses will be just the same with running your own consultancy. The downtime you think you will have to yourself in-between contracts will be eaten up by having to find the next contract. If you happen to unfortunately live in or near a city with a high cost of living, the pressure will be even more intense.