Also be aware that their abuse department shoots first and asks later. I know of servers that were off the grid for multiple days without access because of abuse on a friday - everyone relevant went on weekend.
They _are_ cheap and that comes with a few trade-offs. Doesn't make the product bad, necessarily. If you are cash-strapped and need raw power, buy without hesitation.
Blaming providers for the inability to secure your server is incredibly irresponsible. Unless service was interrupted because Hetzner misread an abuse report for another server (which is highly improbable and most likely is not what you implied in your original statement), you shouldn't ever be pissed that your host took action to prevent abuse from occurring.
things that warrant disruption of service and are defined as abuse:
1) any type of DoS attack
2) phishing
3) malicious activity (ssh brute force, port scanning without consent, etc)
4) cp
5) anything that generates a court order with jurisdiction, including DMCA if you have anything to do with the US
6) spam/spamvertised site
there are more things that can be defined as abuse, but the others are more or less discretionary, imo.
The problem is that relevant persons assisting you in resolving the problem (e.g. giving access using a secure connection) are not reachable over the weekend and take their time. That is a problem of the provider.
If you ignore the 24 hour limit, it will just escalate the case to a support person, who then decides what to do. There is no automatic shutdown, especially not for multiple days.
Not being available for resolution is a different thing.