What are the security risks of allowing administrators to C$ into remote computers on the network?

My last job working at a DoD contractor allowed this but my newer position working at a University does not allow it due to "attackers/malware to move laterally through environments". How common is it that an attacker utilizes moving through systems via C$? I haven't heard of it until the security admin's just told me that.

administrators computers cybersecurity network security security risks