We rank 1 for a keyword that leads just to the homepage. Worried about upcoming website redesign.

So I am to redesign a client website (a dental office) and they currently rank number 1 for "\[city name\] dentist" which is arguably the most important keyword they need to hit on organically. I want to preserve this top rankning. Regardless SEM Rush says most of the organic traffic a month is coming from this keyword in addition to the practice name and Dr. Name to the homepage. Because of this, in the new design, I was going to just duplicate the homepage content and H1,2,3, alt text, meta descriptions for the new website with an updated design. But since none of the other pages experience any significant traffic through organic search or any traffic in general (15+ service pages like 'composite fillings', 'Porcelain Inlays' etc), I was going to remove them or throw 301 redirects (if needed) as they seem to be useless and create new pages that I will use to try and hit on other keywords. My fear is that I know google ranks based on more than just optimized keyword insertion and looks at things like backlinks, context, and if it sees other content on the site mentioning the relevant topic searched. For more context all backlinks I've seen in SEM Rush's report are just leading to the homepage. Would removing and creating new pages other than the homepage hurt the existing ranking as google may be taking context from other pages on the site even though they don't get traffic?