The bit about math homework reminds me of how I started getting better grades in grad school as immediately after I started doing homework in LaTeX. It’s not that I got any smarter, and I don’t think my work improved significantly as a result of using LaTeX. IMO, it was just that my papers literally looked more convincing when they were typeset like preprints rather than handwritten.
I spend a lot of time making my consulting invoices look good, because it seems to justify my rates and impresses the payroll department, who then pays me sooner.
Same way legal departments dress up what are more or less informal requests in high language and good production values.
Old manager coined it "the power is in the template", big difference in response rate between an informal handwritten request & a proper looking 'official' request to comply.
My go to as a freelancer was to buy a nice template (spend $50, it's worth it..) and customize it appropriately. You want something approaching "savvy yet professional" most of the time.