Sure, if you're trying to land a job, the build apps not businesses approach can work (and is possibly better than the opposite approach, cost/benefit-wise). If you're trying to become your own boss, you need to consider the alternative.
Exactly. And a large part of the problem is the way people approach this by trying to find a "new idea." Most businesses aren't new ideas, they're either copycats (nothing wrong with that) or fresh approaches to existing ideas.
A social network for dogs is something that you can't know is feasible before you try it. OTOH a timecard app for remote workers almost certainly is feasible and its success depends on your execution.
If you want to start a business, solve a problem a business has in an interesting way. If you want to build an app, build the most amazing thing you can think of and forget about how to make money with it.
They're not necessarily mutually exclusive. One of the nice things about working as a freelancer/contractor is that you are used to managing your time and possibly working on several projects for different clients anyway. If you choose to spend some of your time developing side projects as well, whether for professional development or simply personal satisfaction, no-one's going to stop you... Just keep the expectations realistic about whether a project is being done as a serious business proposition and therefore justifies the time to develop it properly in that light, or a fun side-project that shouldn't be allowed to become a time sink!