Culinary schools are extremely expensive, and if you can learn on the job, you'll save a lot of money. Learning on the job also allows a young cook to understand much better how to apply techniques to the high-pressure configuration of a kitchen. This will make them better cooks and, eventually, chefs. Many of those engaged in the culinary arts choose not to study and prefer to learn on the job.
That's fine, but if you really want to achieve the highest standards, studying for a culinary degree at a renowned culinary arts school is definitely something you should consider. The opinion that presides here seems to be that it is very similar to a master's degree. Extremely useful with an already solid resume and years in the industry, a poor choice to jump straight into. One caveat in this regard is that you really need to use that title to get jobs that would otherwise be inaccessible.
For example, if you need a little more in your resume for a secondary position or you're looking for corporate positions, a degree is a good option. As is usual with these questions, there is no single answer that works for everyone. The demand for kitchen graduates continues to increase.