No.
You are asking for the ability to commit security violations. Whoever wants this capability needs a course in internet security.
The browser is not allowed to run any downloaded file for security reasons. The browser is also not allowed to unzip the file, since the file could install malware while being unzipped. This is a matter of security, and is also a matter of LAW in many nations, including the US.
The user has the RIGHT to scan all downloaded files for malware before unzipping and running them manually.
The website being browsed has NO RIGHT to install or run downloaded software on the user's computer, without the express PERMISSION of the user.
The browser also might not know how to display the file, since the file type is not known at the time of download. The instructions of what kind of file to create when unzipping are hidden inside the .zip file.
The unzipping function also must use a disk file, not an Internet file. With some compression methods, the software must make multiple passes through the file.