When would this be useful? If your site has a blog with public commenting turned on, links within those comments could pass your reputation to pages that you may not be comfortable vouching for. Blog comment areas on pages are highly susceptible to comment spam. Nofollowing these user-added links ensures that you're not giving your page's hard-earned reputation to a spammy site.
Ask for a technical and search audit for your site to learn what they think needs to be done, why, and what the expected outcome should be. You'll probably have to pay for this. You will probably have to give them read-only access to your site on Search Console. (At this stage, don't grant them write access.) Your prospective SEO should be able to give you realistic estimates of improvement, and an estimate of the work involved. If they guarantee you that their changes will give you first place in search results, find someone else.
In short, nobody is going to advise you to create a poor UX, on purpose, in light of Google’s algorithms and human quality raters who are showing an obvious interest in this stuff. Google is rating mobile sites on what it classes is frustrating UX – although on certain levels what Google classes as ‘UX’ might be quite far apart from what a UX professional is familiar with in the same ways as Google’s mobile rating tools differ from, for instance,  W3c Mobile testing tools.
In addition to on-page SEO factors, there are off-page SEO factors. These factors include links from other websites, social media attention, and other marketing activities outside your own website. These off-page SEO factors can be rather difficult to influence. The most important of these off-page factors is the number and quality of links pointing towards your site. The more quality, relevant sites that link to your website, the higher your position in Google will be.
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