I completely agree that it is as much a problem of usability as of accessibility and both are important. Even if you just adopted the big stick approach, you should not have an option on accessibility, since it is a legislative requirement in many countries now.
If someone is scanning text, then a single word here is not highlighted or registered with the keywords you are looking for. Especially now, with the style of sites without underlines for the links (the general idea is to let readers know that it is a link: if it looks nice it is important but secondary to understanding, and color alone is not enough). If you underline the phrase, which should directly indicate the content of the page to which the link goes, that makes it clear to the reader what you will get when you click. Just apply the director of Steve Krug "Do not make me think": people just want to get to their destination quickly without thinking much about the trip there, and their job to create that site is to help them succeed.
By the way, accessibility problems affect many more people than those who use screen readers (and more than the problems at sight). 10-20% of the population has poor vision and it is more difficult to scan that the linking words stand out, what simply using here does not work. The growth of access to the web on phones has only increased it enormously, since by seeing, let alone trying to tap, a small word is really a poor usability. That is a very important part of anyone's target market to decide that you do not want to be a potential customer just because it makes it more difficult to use your website.
None of that means that your site can not be attractive, but people do not mainly go to a site because they like what it looks like, it is to do something. Using words that are scanning will help you do this.