If you delete a website in ISPConfig and you then want to re-create that site with the same name, all you have to be sure of is to empty ALL recycle bins.
If you don't empty the recycle bin, it could create some confusion, but this should not be a reason to re-install. Unless you 100% want the same match between webnn_whatever and you domain name. But that's personal.
To "start over" with what you describe should only be to delete the websites, both in ISP manager and DNS manager, empty ALL recycle bins (and carfully find them all: I needed new glasses once, because I overlooked one recycle bin) and recreate the sites. No need to re-install ISPConfig.