Is it safe to reinstall Windows 10 on an infected pc using a not infected boot USB flash drive?

I have two PCs: PC A infected PC B not infected I created a Windows 10 boot USB flash drive on PC B with the tool offered by Microsoft. Assuming that the boot USB flash drive is not infected and that the viruses, malwares etc… on PC A are only on the hard disk (not on the bios, firmware etc…), it is safe to format the infected disk via the boot USB flash drive (with subsequent reinstallation of windows)? That is: Is there no way that viruses/malwares etc… from PC A's disk infect the USB flash drive during PC A booting (and formatting and reinstalling Windows) via the USB flash drive itself?

Question by drip on Super User, licensed CC BY-SA. We show a short excerpt and link to the original thread as credit.