I don't see how it can be a copyright problem to allow people to save it privately. Especially since every copy is deliberate, i.e user chosen to save that particular page.
It can be. Providing the tool to do something illegal, with the sole purpose of the tool being to do something illegal, is illegal. Check out the YouTube DL project history/controversy.
Browsers provide the tool to save those pages (ctrl+s), in what way is it different? Honest question, as I'm building something that could be impacted.