Briefly describe your issue below:
I’m only able to run airmon-ng and airgeddon using sudo:
sudo airmon-ng
Why I am not able to run these without root privileges? Have I installed the software incorrectly and is my system more vulnerable to problems?
Correct. The airmon suite of tools can change the adapter options of the WiFi cards and change how they normally work and this requires administrative rights, which in Linux systems is root. So there is no problem, install is correct and it seems everything is working as it should.