This is such a brilliant point. I find the coder "puritanism" leaking into startups and I can't say I agree with it.
Starting a business has been done in many ways. Having been in business for 15 years I have gotten to meet a lot of other small business owners and there is as much variety in how established businesses came to be.
Having this delusion of its only a "real" startup if you do it this way is hogwash. So many great businesses were built on hard work, sacrifice, long hours, juggling more than one thing at once, until the new business could stand on it's own two feet.
Knowing when, and what your new business needs (more time, stepping away from other obligations) is a critical skill. Simply committing all of your time to one thing without a wider business, or varied experience can in some cases be a detriment.