Is it possible to not have apps saved in your iTunes library?

I have tonnes of apps on my iPhone, but why do they have to be on my laptop's iTunes library? It's not as if I can use the apps on my laptop!

If I just delete all my apps in iTunes, will they be removed from my phone? Does the app need to even be in my library?

If not, how would I be able to stop iTunes from automatically downloading them and waste all of my memory?

Probably the iCloud

The reason for the apps being stored on your iTunes library is so if you need to wipe your iPhone you would have a backup. The apps would restore on your phone with all of the data in them. If you don't want to back up to the iTunes library on your computer, turn on the iCloud backup on your phone. This will backup everything directly to the cloud, bypassing your computer.
To turn on iCloud, go to
Settings---> iCloud---> (make sure you are signed in with your Apple ID) --->Storage and Backup--->iCloud Backup ON--->

When you turn this on, your iPhone will automatically backup to the iCloud whenever your iPhone is plugged in and connected to Wi-Fi.

Hope this helps!