Most of my admin account are licensed, since I add an EMS E5 license to many clients on managed plans, so I can get my "SIEM-like" alerting thanks to features of the EMS E5 license. I also often put in an M1 or E1 license....(don't need the apps)....for clients that I more heavily admin and manage, so I can get to Teams stuff. Of course, accounts are long in passwords and under MFA.
But I don't use names like "admin". Do you specifically need the name "admin"? In which case you can get some email forwarding capability by creating a contact for your external email, and then doing a distribution group by the name of Admin and forwarding to the contact.
Or you just talking about..having whatever you admin account is called...send emails?
Don't forget, non profit clients can get free online only licenses....in case the client(s) you're talking about are non profit.