Even with Linux to install stuff you may need to use sudo and run the package installers as root. Because they may need to write to locations or modify files a plain user can't.
But even software installed without admin privileges can try to elevate its privileges later if there are vulnerabilities or if in some ways it can intercept credentials.
Linux is safer now because most applications are installed by trusted sources. If people are lured to add a warez repository to their sources list - good luck...
The compromised installer is one of the best way to deliver malware - you don't even need to try to exploit vulnerabilities, you mostly need just to evade AV detection. Then you run with enough privileges to create havoc easily.
Anyway, it's quite simple to run Windows as a non-admin without an IT department behind you - you'll just need to use the "Run as Administrator" command more frequently - just like you often need to use sudo in Linux to perform some tasks.