- no remote access to the console if ssh stops working
- no possibility to remotely power it down/up
- if the hardware dies, no possibility to restart on a different hardware remotely
There's nothing wrong with a home server, I have one or three myself, but these limitations are why I move "essential" services (e.g.: email) to the cloud.
Home servers are better suited for exactly this, need of high CPU, and also need of a lot of storage, for a backup server for example. I used to run everything on home servers and back them out to the cloud, but I have now started to reverse this, run the services in the cloud (cheap for small service, remotely accessible etc...), back them up to the home server (cheaper large storage, it's fine if they go offline for a few days while on holiday for example).