Oftentimes, poorly-managed VMs / VPSes get infected with scripts / botnet software and start blasting out spam. It takes a long time for IP reputation to recover, esp. under the same owner info on the netblock.
Regarding inbox deliverability from dynamic IPs (like you'd have with a residential connection), it might work sometimes for short messages with no attachments to people you've corresponded with before, but I wouldn't expect general deliverability to be very good. You have the same problem with botnet infections / malware-based spam here as well; home PCs are much more likely to get infected with that kind of stuff (though WordPress exploits are VERY common on servers), so many people running mail servers will just straight up block dynamic IPs from big ISPs and assume that nothing of value was lost. Personally, for low-volume mail such as what a home server might send regarding maintenance or alerts, I'd recommend using a service like mailgun and hooking up to that with SMTP. It's a lot easier than running your own mail server, you won't have to deal with inbound spam if you're only sending, it works well with minimal setup, they guide you through each step, etc etc.
