That's the theory behind side projects, but it's a false dichotomy.
Side projects are, by definition, something you do on the side. Your primary day job requires attention whether or not you do any side projects. Side projects are additive on top of the work of your day job, but subtractive out of your pool of free time and energy.
Side projects always start with good intentions of broadening horizons, but people generally realize that they only have so many intensely productive hours in a day. Do you allocate your most productive hours to your job? Or to a side project? It's tempting to say "both" but in practice that will spread someone's finite energy too thin across both domains.
Students tend to go wrong when they think that side projects are the key to unlocking their next big job opportunity. When they start to burn out in their dayjob, they think they're just a couple of side projects away from qualifying for an opportunity that will make them happy. The trap is that being burned out at a dayjob and adding the additional work of side projects only worsens the burnout. They get stuck thinking they need to finish the side projects before they change jobs, but they can't complete the side projects because they're too burned out from jobs and a side project. In these cases, I encourage people to drop the side projects and just apply to jobs. It works better than most people expect.