BPF cannot be collapsed always in classic UI, but possible in UCI like popout behavior or flyout without expanding. It needs some unsupported DOM manipulation in classic UI to nullify the click event of stage chevron or simply user training not to click it at all. Or better create a similar UI using webresource if you want.
It fails the original purpose, and re-purposing the BPF raise these kind of questions. If you have built the necessary business logic already in some other means - then custom UI is better choice rather than bending the BPF.
BPF is for guided process advancement, we can add attributes/entities as steps to move forward and enforce the field value requirements for reaching next level. I know some clients use them as tabs, some use them as just chevron tracker, so they don't want to waste the real estate under the BPF as they don't need any fields under the stages.