To give better advice, you should provide more information regarding your Ph.D. journey. For example, who defined your dissertation topic and whether you're supported financially during your studies? I try my best to cover all cases as best as I could.
- First, if you've previously (i.e., before your final defense) talked to your advisors about publishing parts of your dissertation, one might consider it bad faith if you do otherwise. One of the professors in my department still complains about a student who didn't deliver on the promise of writing the final paper of her dissertation after about 5 years.
- If you want/need to maintain a good relationship with your advisors (i.e, work on joint projects, co-supervise students, etc.), what you intend to do is usually a deal-breaker.
- I suggest that you check with your alma mater for their intellectual property regulations. Some institutions prohibit you from publishing work done with their money and equipment under another institution affiliation (as you're a professor someplace other than your alma mater, you might intend to put your new affiliation on the paper).
- Some institutions do not include papers directly based on your Ph.D. dissertation in your tenure request evaluation. If that's the case in your current institution, what you intend to do would benefit you only in terms of reputation in your field.
- If you're not experienced enough to publish your paper in a good-enough journal, your advisors might be able to help you with that. Their help might come in handy as one usually doesn't have any other person to read the paper critically and help with the revisions. Also, if prominent scholars, their name might be able to help you as well.
A simple compromise would be to write not all the papers with your advisors. If your experience with the first paper was positive, you might re-evaluate the whole situation differently.