The problem with this approach is that while the team that is spending their budget on your salary probably doesn't give two shits about an extra $5-20k/yr the disconnected HR department has always been laser focused on pushing back on salary numbers for some reason.
I interviewed at a place where I knew someone who worked there and knew exactly the number they were looking to hire at, I named that number in my interview and they still tried to undercut me. I said, no I want $original_number in my response email and they caved in literally 5 minutes. Why?!?!? You found someone willing to take the job at exactly the team's budget. Shouldn't you be popping the champagne that it's painless and everyone's happy?
The hiring team and the HR team have different local incentives. The hiring team just needs a position filled within a specific budget. The HR team is doing its best to manage company wide expenses. So it is worth it to them to take a crack at reducing the cost of a hire.
If you can identify a company's inconsistencies in policies or behavior, you can identify different sets of incentives different parts of the company are under.
I interviewed at a place where I knew someone who worked there and knew exactly the number they were looking to hire at, I named that number in my interview and they still tried to undercut me. I said, no I want $original_number in my response email and they caved in literally 5 minutes. Why?!?!? You found someone willing to take the job at exactly the team's budget. Shouldn't you be popping the champagne that it's painless and everyone's happy?