You would have no issues redirecting all http pages to https. Https is not mandatory for any website, unless it has a members area.
However, if this is a website that trades traffic with others, you might have issues with passing the referrer from https to http, so your traffic might not be tracked on your trade partners' side if they haven't updated to https.
An alternative is to keep both http and https (without forcing) if you set up canonical tags to point to https version of your pages.
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