A lot of the problems I had to deal with on a daily basis at the School I was able to solve with standardization - but the only practical way to roll that out was through a consistent imaging and deployment system. We went with SystemCenter because it was effectively “free” for us, but pretty much any competent solution will do.
Rather than running around to chase folks down to get their machine and install software, we had a self-service software library. Since all the machines were the same and used redirected desktop/documents, when a device failed rather than having an emergency repair or reload all I had to do was check out a machine from my spares pool to the user and their old machine would get checked in for repair.
Then, frankly, the other way I managed my workload was by saying No a lot. People would commonly ask IT to do labor intensive work to save a couple dollars vs. buying a proper solution that would both be more appropriate and long-term supportable. Rather than spending hours refurbishing old, outdated projectors when they failed we’d just buy new or run the broken unit over to the warranty center. We didn’t support user printers except where privacy required it (principals, finance, etc.) and only supported quality hardware.
tl;dr: not spending money isn’t the same as saving money. Spending money on quality hardware means less time spent doing end-user repairs, and less time they can’t work. Spending time/money on automation means less time coordinating and performing menial tasks. Spending time/money on training means less end user support. Etc.