Invited contributions have some advantages, especially after tenure.
(1) Rejection is not as much of an issue. I've never been invited to submit something and then rejected.
(2) You can still get feedback, but you aren't necessarily anonymous so you can cite your own work freely.
(3) It is nice to be invited. It shows your work is valued, or at least you are on the short list of people invited in a particular sub-field.
(4) Invitations are usually for special issues of journals or books that are less random than non-special issues of journals. They are more likely to be read by specialists in your own field.
(5) The article is often published in a journal that is usually refereed. Thus it essentially counts as an article in a refereed journal. (Even if you put an asterisk beside it.)
(6) It provides a stimulus for writing an article, and external incentive.
There are some drawbacks too:
(1) If you aren't careful, you can relax your own internal standards. They won't reject you, after all, so you don't have to be quite as rigorous with yourself.
(2) The level of critique you get might not be as rigorous either. You might miss out on the opportunity to improve your work.
(3) You can easily begin allow other people determine your research agenda. (I could do little else but write articles in response to invitations, if I wanted to.) You can justify it to yourself: I would have written this anyway, right?
I have no idea how many articles I have written by invitation. I could look at my cv and tell you, I guess. I'd guess it is a lot, more than half of my total number of articles. I don't regret any in particular, though I might have taken more control of my destiny at times.
Invitations are the elephant in the room in any discussion of peer review. If a lot of articles are published through invitations, then peer review becomes much less attractive to senior scholars like myself. If I am reasonably confident that I can write a good article without the "help" of an anonymous reviewer, who may or may not help, then I can side-step the process almost completely by publishing almost exclusively by invitation. Then the only people having to subject themselves to peer review are junior scholars too new to the field to be invited a lot, and who need the stamp of approval of peer review for tenure.
I actually got a lot of invitations even before tenure, so my case was a mixture. I did go through the process of submitting and being accepted or rejected, but very quickly I also began to get invited too. I don't remember a long period of being an unknown.