Not in my experience they don't. I use OVH and nfoservers and I've had an issue like this exactly once on both hosts.
On OVH one of my servers was hacked and running typical scripts that are run once that happens (port checking, common admin credentials, brute force attempts, etc)
They cut off all internet access to and from the server and sent me an alert stating what was happening and that I needed to VNC into the server, resolve the issue, and let them know how/why it happened and how I resolved the issue. Once that was done they just removed all the blocks on the server and we all went on our merry way.
Edit: To clarify the VNC console is on their site, not a remote connection.
I run the IPFS daemon on Hetzner, and it was trying to connect to local IPs because of some misconfiguration. They sent me an email saying my server was portscanning their LAN, and I should fix it and email them how I fixed it.
I didn't know what they were talking about so I replied saying that, they helped me shut down the local port connections and I never heard another complaint from them. There was no downtime or banning at any point.
Hmm, I've done lots of stuff on OVH that other hosts consider abusive, with nary a word of complaint from OVH.
OVH seems to have this whole automation thing down cold, monitoring boxes for dying components and letting me run hog wild on their VMs without limit...
The one time I used their phone support, the guy I got was fairly helpful. They seem like a hands off company overall.
Far from flawless. They did it to me and it was dropping half of DNS requests I was receiving so my websites were down. And you practically have to beg them to take you out of DDoS protection.
This doesn't seem unreasonable, OVH is not advertising DDOS protection (nor do they seem to be structured to offer it). Some hosts will can your VM and throw out its data, which is a much worse outcome.
A machine on a GCP project got compromised. GCP emailed us right away and we fixed the issues promptly. No outages, no arbitrary suspension, and no grief apart from the compromise.
Hardly fly-by-night.