At best this is monitoring and playing whack-a-mole on their part which they've done a pretty good job of by the looks.
Also, although I have many things to blame OVH for, they at least take a somewhat proactive stance regarding security, even for the very cheap dedicated servers. They usually contact you when they notice a traffic spike on unusual ports for example.
But yeah... judging by the people I know in real life who own cheap OVH dedicated servers, I'm not surprised at all by these news.
I'm pretty sure 90% of the customers are not professionally trained in server maintenance. I am, and I don't want to do it anyways unless I have a good reason to do it.
The hard part was to set-up all these services, keeping them up-to-date, since no other party depends on them it is considerably easy and almost risk-free. Other than that is not time-consuming at all. Only 2 times in 3 years I had to re-configure a service. Most of the times I just run an upgrade-script on a tmux session and everything runs smoothly (I rarely use pre-compiled packages).
Now, if I had a production-level web application, I would probably set-up as carefully as I could a new VPS and roll my application there, up to the point where I needed to scale.
If it would be a one-man-show I'd probably go with Heroku (since I write sinatra/ruby/rails applications) or similar (possible cheaper) service to avoid spending time on sys-admin. But these service IMHO are still, expensive for projects with no income while a VPS can do all that and mode at once at a considerably lower price.
ps. As a side note. Before I join HN, I though that all programmers were capable of sys-admin (UNIX servers). Then I realized that tasks that seem trivial to me, are considered somewhat difficult for others and vice-versa of course.
The company I currently work for have to full racks in two data centres each, most of which is near idle and it's a full time job for 2 people. Could do away with all the machines and all the associated administrative staff, just use a devops team and shave 40% of capex and opex as well by moving to something else.
But then again, they might not be getting nice lunches with HP and the DC vendor.
If you're asking about the hosting company, they largely don't care what you do unless someone complains.