Are broken and external links very harmful to site optimization?

Are broken and external links very harmful to site optimization?

While working on the inner pages of my website I came across a number of broken external links. I realize that many SEOs advocate against broken links. However, changing these links would mean I would have to change the entire inner pages of my website. And there is hardly any time or resource at my hands to spend on the correction and maintenance of these links. Is it essential that I repair these links immediately or can I postpone the task to further notice? I would really appreciate your opinion on this matter as it would help me create a more optimized website. Please feel free to share your ideas.
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Digital Marketing Agency|Seo UK