> Management said we don't have enough money to fix any of this.
It's often even worse. Many years ago I was responsible for backup a DEC Unix system. Asked for funds to conduct a disaster recover exercise to find out if our backups worked and was turned down even before we had tried to work out how much it would cost.
I often wonder what proportion of backed up files and systems are actually in a state to be restored and have the necessary tools and expertise to do it in a timely manner.
An even worse problem in some places, including the one I worked at, is a tendency for users to assume that backups are kept forever and for the management to totally neglect archiving of important documents such as specifications, drawings, and design calculations of products that have an expected lifetime of over fifty years.
I had to inform several users that I could not restore the file that they had only just noticed was missing because it was last seen more than two years ago and presumably disappeared longer ago than our longest backup cycle which was one year of monthly full backups.