Truthfully I doubt there will be much you can do - I too have similar issues where the business largely do as they wish - don't want a DBA until something goes wrong but still won't allow any control. I usually refer to these as "Wild West Servers" sorry to USA members!

I think to be honest that if it gets to you then you seek out another job if you are an employee because you'll always have conflicts within yourself as you try to do what you know should be done vs the silly demands/expectations of the business.

There's also the phrase "You can take a horse to water - but you can't make it drink".

I raise the risks of unmanaged servers to the business ( every time I have to fix something ) but ultimately I suspect little will change until someone at the top forces the issue or a system is lost big time, but even then I'm not sure.

( I hasten to add that the main system I support/manage is heavily secured and as a consequence suffers little disruption )