Sure, but this solution won't be integrated well into Apple's ecosystem. Even connecting to shared file storage is still a bit messy in macOS, it just doesn't feel right compared to iCloud Drive.
And I think that's done intentionally, so users won't dare to own their data and host everything locally. It's easier for NSA to access your data when it's offloaded to some cloud server... okay sorry for bringing up the conspiracy theories.
Disagree
Mac mini has limited space inside. It can fit up to two 9.5 mm drives. Any 2.5" drives of 3 TB or higher capacity will be thicker, usually 12 mm or 15 mm. It's possible to fit one "the hard way", but that won't look nice.
Also HDDs tend to fail, while SSDs are not. Higher upfront cost of SSD will be compensated by lower power consumption + you won't have to urgently replace it after 5 years when the spinning rust dies. Flash storage simply saves money in the long term.
Plus, SSDs are silent and don't vibrate, so you don't have to hide that server in the closet; you can keep it visible and even sleep alongside it.
Where 2012's Ivy Bridge consumes 5W, 2018's Coffee Lake will consume ~3W, M1 will consume less than a watt, and Raspberry Pi 5 probably even less than that. Multiply that by 365 days of uptime and savings might become noticeable.
And I feel sorry for them! They get lacklustre movie playback experience (no 24 Hz support, no color space matching, no Dolby Vision or HDR10+), wacky interface that's not optimised for the big screen, lack of HDMI-CEC support and many other inconveniences. It's a thing of the past. Just use Apple TV instead.