An Intel based Mac mini without the T2 Security Chip (2014 or prior) can be configured without FileVault encryption enabled. These you can easily SSH / ScreenShare as there won't be any pre-boot authentication login screen because the disk is not encrypted at all and the operating system boots immediately on power up.
Any Intel w/T2 or M1 Mac mini (2018 -> 2020+) will be encrypted at the hardware level with the Secure Enclave chip on the T2 / M1 SoC (System on Chip). The SSD is encrypted at time of manufacturing and the encryption cannot be turned off. When these Macs boot, they require physical access to unlock the disk to boot. There is no automatic login option either. If you enable FileVault you merely add a recovery key. When turning FileVault on or off there is no encryption nor decryption of the drive sectors. The sectors are always encrypted. FileVault gives you an extra recovery option if you forget your password you can still boot with the recovery key and reset your password. The recovery key is stored in iCloud by default.
If FileVault is enabled you can reboot with 'fdesetup authrestart' which is what happens when applying macOS updates, etc. But you need to remember to set that option before the next reboot. So planned reboots mostly. I suppose you might be able to automate setting 'fdesetup authrestart -delayminutes -1" meaning it shouldn't immediately reboot but wait indefinitely until the system does restart. This works, I just tested it out. You can also pass in an '-inputplist' which would be an XML file containing the user and password to use when authrestarting. You could script that and perhaps use Launchd to apply it at every boot. The setting for authrestart is one time only so you need to set it every time you boot to ensure it will work on the next reboot. Doing such a thing has its security risks as you are effectively bypassing the disk being locked at boot.
If you are losing power for upwards of 4 days you should be using a generator and a UPS. The UPS will maintain power until the automatic generator kicks in. If the UPS detects power loss, you can execute scripts to automatically shutdown before the battery runs out and perhaps again, insert the authrestart command for a one time bypass of the disk encryption pre-boot authentication. If the generator kicks in, the shutdown will not occur and the UPS recharges the battery. When / if the generator runs out of fuel and shuts off the UPS keeps things running as long as it can before safely shutting down the system. When power is restored, the authrestart should work if you set things up properly. Crisis management process is to test these things perhaps as often as once or twice a year. Generators require regular maintenance as well. The big ones need frequent oil changes, etc.
The Apple T2 Security Chip is actually a repurposed A10 iPhone SoC processor running a specialized operating system called BridgeOS. It has the same Secure Enclave in all iPhones and iPads. All of these mobile device SoC processors have encrypted file systems that are always encrypted. The M1 is a larger scaled up version of the mobile chip designs. That is why mobile Apps can run on macOS, the processor is almost identical. There's just more cores, RAM and more bandwidth, etc. On Intel w/T2 Mac's the T2 boots first then passes control to the Intel CPU. On M1 Mac's it's all the same chip.
The hardware encryption is, I suppose, an artifact of using the same chip design as the mobile SoC designs. Most of Apple's sales are notebooks not desktops. They sell far more MacBooks than iMacs or Mini's or Mac Pro's.
You would be surprised how much personal information would be useful to malicious bad actors that can be found on any computer. Even if you don't have confidential company documents or defense contractor top secret data. Your keychain might contain sensitive passwords, your browser history can reveal a lot about you as a person. Your autofill data would be potentially useful. Your friends, family, and contacts can definitely be useful. Knowing details about your family and pets might be enough to get past security questions, etc. Having ones identity stolen is a horrible experience and results in a new full time job to combat debt collectors and rebuild your credit and never discarding all the documentation as the troubles can re-occur years later as debt collectors sell their records to others who start over with attempting to recover the debt.