It generally does NOT make financial sense to be self employed unless you can absorb the risks involved. That means one spouse could try to start/build a self employment income if the spouse can cover the household financial needs. It means that people with children, or aging parents, likely should not try self employment unless the household income can cover both the immediate needs of the household and the potential needs of others. It should also be a good time economically for new business openings. You should also be capitalized, with enough startup capital and reserves to build out and live for 6 months or more.
You should have a unique set of skills or education that makes what you plan to offer unique. Licensed professionals with a following/client base could do this, as there is limited competition for clients.
People who do this should have enough experience in the field to know what to expect. A restaurant should be opened by people with years of restaurant experience in all facets of the work, from dishwashing to cook to up front greeting of people.
You will likely find more satisfaction in working for yourself, from the effort to the income to the prestige. But you had better have a substantial work ethic and the health to work long hours.
You should be a correct age to take these risks. becoming self employed in one's 40's or 50's may be too risky, since losses might be difficult to recover from.
It can make financial sense, but only if you can overcome the hurdles listed, and there are certainly more. Your spouse/partner must be willing to assist. You must know how to develop new business and be able to secure the work and complete it professionally. You should have a sense of issuing credit, stopping work for customers who are no pay/slow pay. You must be able to run your business like an owner and work your business like an employee.
If you can meet these hurdles, then self employment does make financial sense.