I hope every completion done inside minibuffer is repeatable by vertico-repeat, including commands invoked by M-x. Vertico, however, didn’t include execute-extended-command as a repeatable session by default. You can be seen it by examining vertico-repeat-filter variable. So I have to customize it like this in Doom Emacs:
(after! vertico-repeat
(setq vertico-repeat-filter (remove 'execute-extended-command vertico-repeat-filter)))
The question is execute-extended-command seems to be a reasonable default completing session, why does vertico excludes it?


execute-extended-commandis excluded for the reason that I didn’t find it useful to repeat. If you type M-x you get the recently used commands sorted to the top anyway. As an often executed command, M-x pollutes thevertico-repeat-history. You can browse the history withvertico-repeat-select. But if you dislike this default, it is easy to customize it.