A regular job with regular income looks good on paper if you want a bank to lend you money, for example.
Maybe less likely to appear on tax authority's radar for undisclosed income if people know you as Joe the IT guy who leaves for work at the same time every morning?
Source: I worked at a bank, and wrote algorithms for loan acceptance which evaluated such things.
I would never discourage anyone from self-employment, but right now I'm watching a good friend try to get a mortgage in Germany... and he's been running his own company for 20 years... in a highly volatile industry... and let's say they'd be treating him a whole lot better if he had a boring day job at some big company.
If you're planning on stuff like mortgages and (depending on your passport) visas, "regular old job" is worth many multiples of self-employment. If your self-employment makes enough that you won't need a mortgage (etc.) then great, but I would bear it in mind when thinking about quitting the day job.
I would, especially if they are in their prime earning years and are trying to become independent contractors. Software engineering jobs command high salaries and benefits these days. The opportunity costs are just too high and the odds of sustaining a one-person contracting show for 5, 10, 20+ years is slim to none.
The only real risk is that during economic downturns it may be hard to find contracts but your employer could fire you as well.
That's just one factor. Banks are looking to minimize risk and from the perspective of banks, self-employment increases risk. That's not to say banks won't loan to you, just that the hurdle is much higher for you to prove that you are not a risk. Chances are your interest rates will still suffer even when a bank decides to loan to you.
I actually do think keeping the job is a good idea for exposure to different ways of thinking, but perhaps scaling it back a little (part-time?) in order to invest more time into the primary income source.