What do you get for all this trouble?
It's hard to quantify but worth looking at.
Better processes and better tools make for a more attractive and sustainable work environment. This is beneficial if you are trying to attract and retain staff. Isn't everyone?
There is reason to think that better processes and better tools lead to better outcomes. Primarily because they just work better, but also because the people using them have less friction and can perform better. Seems like a snowball effect - less friction in the work, better results, buoyed by this sense of accomplishment to even greater results.
So you can look at the direct benefit of better outcomes. You can look at how it increases the attractiveness and retentiveness of your organization. You can even take it a step further and consider the ways in which it decreases risk.
So what am I asking you to change, specifically? What am I asking you to do? Fix your software. Put people first. Incorporate innovation.