Some application installers force the installation of shortcuts. But the average program will give an option to install or not to install any kind of shortcut. Need to keep both your eyes and mind active about the program installer options before pressing that 'continue' button to proceed with the installation.

Are you referring to folder shorcuts or program shortcuts?

Windows 10 has a few methods to use in regards to opening a program. Perhaps the Desktop method of opening a program does not suit you.
I am guessing if instead you used alternative methods away from the Desktop to open programs and folders then this might solve this long term problem you have with shortcuts. Your reliance on using the Desktop appears to be your problem when you do not fully understand how to use it faultlessly.