To add to this, when I was trying out CFP, I found it annoying that there was no explicit "build" button. I changed the default branch that I wanted CF to build from, but it didn't automatically make a new build. And there was no button I could click (like there is on Netlify) to say "rebuild now".
+1 for this. Netlify has it and I have used it many times to redeploy a site after changing some config settings (e.g. env vars, build commands). Having git push as the only deployment trigger is a pain in these scenarios.