1. there are no system admins present, only 17yo kids who got hired to sit there and do nothing while players cheat so the tournament org can pretend they did something.
2. you dont need to install a cheat. look up cheat injection, badusb, there are millions of ways to run a cheat when you have physical access to the pcs, or access to the internet. at most tournaments, players get both physical access to pcs and open usb ports in front of them, and internet access, at least to valve servers, which btw you can also upload cheats to if you get creative.
if tournament orgs took proper security measures, put pc's in locked boxes that players cant get into, and didnt give any public internet access on the lan pc's, then you would be right. but they dont. so, the question becomes: why dont tournaments take proper anti cheat measures, and why isnt anti cheat ever in the news here on hltv.
i can only think of 1 good reason and thats that tournament organizers dont want to catch anyone cheating. it wouldnt be expensive to do this properly. they just dont want to do it. its not in the financial interest of a tournament org to catch anyone cheating. it would be detrimental for them.
my conclusion is that tournaments and valve are letting players cheat and dont implement anti cheat measures to maintain plausible deniability and to continue making a lot of money.
in that situation, it is very easy to cheat. you literally have to be indian, use a detected public cheat from the internet and rename it word.exe to get caught. its that hard to get caught.