Not only are they annoying, but they can be downright harmful to your website. And it's not because you don't want them to be associated with your brand: if you have too many backlinks from spammy sites, search engines can penalize you, even if you're completely innocent of any crime. Getting backlinks is an essential part of external SEO, and getting more backlinks is called link building. But like many aspects of SEO optimization, link building isn't easy.
Most backlinks are good, some are great, and some are toxic. Too many toxic backlinks can damage your rankings. Yes, you can have too many backlinks, although this also depends on the niche and the competition. Some niches are so competitive that you won't be able to position yourself without a lot of links, although there's a fine line between enough backlinks to position yourself and too many backlinks.
Too many backlinks often cause problems such as de-indexing, Google penalty, manual penalty, or irrelevant backlinks, and are extremely difficult to index. Yes, it can be beneficial to have more than 1 article with a link from the same domain.