I work with a lot of clients (especially now that COVID-19 is a great thing) who can't understand my recommendation that their site needs to be completely modified, repaired, or redone. They are pushing for more and more marketing ads, but don't realize they will never get the right conversions. When I explain this to you, how they should optimize and even do a proper UX test before they can expect conversions, they will close nine out of 10 times and will only require more ads.
What robust options are there (in terms of methodology or tools) to help convince website owners that they need to design tweaks or reworks or brand new websites when they don't seem to want to listen?
Some tools like GTmetrix have occasionally helped convince people that "your site really sucks", but other than that, I haven't found any solid tools that really go the extra mile in this regard. Just logic and simple experience, even when more than 20 years have passed behind you, don't help people appreciate your wisdom either, unless you have some supporting data that specifically relates to your situation.