A part of me dies everytime

I see people having to beg others to review their PR.

Hint: the problem is systemic and not about the lack of accountability/responsibility of reviewers.

Try tweaking the process so that the availability of the reviewers is guaranteed by default and they are not frequently faced with having to trade-off between “working on my code and being in the flow” and “getting interrupted and reviewing other’s work”.
A win-win.

You got it. Pairing/Mobbing.