There's nothing wrong with self employment in and of itself. I've been self employed for many years now, and this hasn't stopped me constantly receiving jobs offers. Of course, I've also been employed for many years before that, and that probably counts too.
I think self employment only looks bad when it's interspersed with very small periods of employment, from a couple of months to six months. Having long periods of unemployment, followed by short bursts of a couple of months here, three months there could maybe be interpreted as a sign that the candidate has a problem with keeping jobs, and that there are probably good reasons for that.
Having only ever been self employed could also be seen as a bad sign. Having never worked within a company, maybe the candidate has no teamwork skills, cannot work within a hierarchy, cannot keep a fixed schedule, etc.
I can't think of any other situations when self employment would look bad.
May I ask how employers are even finding out about you to give you these "constant" job offers? I've been a solo project guy for a long time and feel like employers are unaware that I even exist.
I'm going to guess your resume has a Google/Amazon/Facebook name brand on it somewhere.
LinkedIn and personal recommendations mostly. I have absolutely no "name brands" on my resume (I stay well away of large companies actually), but have a somewhat productive network I've nurtured over the years, which is where I also get 90% of my freelance projects. I also happen to live in Romania, where there's no way to go hungry if you are an even remotely competent developer or other type of IT professional, because the demand outweighs the supply by a huge margin here. Living in the capital (Bucharest) also helps, since the vast majority of IT companies have their offices here.
I think self employment only looks bad when it's interspersed with very small periods of employment, from a couple of months to six months. Having long periods of unemployment, followed by short bursts of a couple of months here, three months there could maybe be interpreted as a sign that the candidate has a problem with keeping jobs, and that there are probably good reasons for that.
Having only ever been self employed could also be seen as a bad sign. Having never worked within a company, maybe the candidate has no teamwork skills, cannot work within a hierarchy, cannot keep a fixed schedule, etc.
I can't think of any other situations when self employment would look bad.