Is it really necessary to use touch id with a mac mini?

Touch ID is an optional to use feature. You aren't obligated to set it up. So, no, you don't really need a keyboard with the Touch ID feature. Most any basic keyboard will work with your Mac mini.

But as @FoxFifth has posted, the Password app cannot be used for Mac login. Applications cannot be accessed until after you have signed in to your Mac.

Just enter your user password. I don't have anything with TouchID on my M4 computer. I am using a 12 year old keyboard with wired mouse.

The Passwords app cannot be used for user login to a Mac.

Also note that even if you do have a keyboard with Touch ID and have Touch set up, you will still have to manually key in the login password the first time you login after a shutdown.