It depends on the deal you strike. Mark Zuckerberg still controls Facebook even though it is a public company despite selling a bit here or there if he wants cash, borrowing against the shares, etc.
Other founders lose control of the company at an early stage. Many people would be delighted to get $5-50M worth of stock in a quality public company and be free to do something else with their life.
VC and accelerators offer benefits by association. For instance I worked at a startup that used space at an accelerator for B2B software startups close to Union Square in New York City. It was energizing to be surrounded by people who are thinking about both the software development and marketing aspects of the business, there is the network of the people who run the accelerator and brand name which helps with finding customers, hiring. You can walk out of that office and hike (or take the subway or a car) to meetings with mega finance, media, consumer brands, you name it.