The crawl by Googlebot will be more efficient if it can go directly to the destination page rather than having to go trough a redirection.
There is some discussion whether 3xx redirections do have an impact on page rank / page authority - Google official point of view is that it doesn't.
Redirects do however indicate have an impact on speed (check here: https://developers.google.com/speed/docs/insights/mobile: "we strongly encourage webmasters to minimize the number, and ideally eliminate redirects entirely" - context is mobile but is applicable on all redirects) - but again for most sites this won't make a huge difference on total load time.
I doubt that simply cleaning your site and removing the 301 will give a boost to your search traffic, but it just something you need to from time to time (idem for internal 4xx errors) to improve the general health of your site.
Dirk
PS I am a bit puzzled about the remark "auto redirects" - you must make sure if you redirect that you redirect to a page which is similar to the page that has disappeared. Google considers most other type of redirects as "soft 404". If the page never existed - like domain.com/kklfjklgjkldfjg - it should return 404 and not be redirect.