Hi there!
From my experience, the best results I was ever able to achieve for a Client is when we consolidated all URLs to a single URL solution. Canonicals are amazing, no doubt. But I've experienced a canonical structure being ignored if there are instances where the canonical structure isn't 100% 'correct.'
If there is a way that you can have your website navigation & internal/XML sitemap reinforce your preferred URL, that would certainly reduce the number of URLs Google would crawl. Then, if you permanently (301) redirect all the now non-navigable URLs to the single preferred URL, you should see a significant boost in traffic (from consolidating all of the authority into a single page, now reinforced throughout your entire website).
If that's not possible, and you have to have multiple URLs within your site for budget/platform constraints, then yes, let Google crawl them. Otherwise the algo won't be able to see your canonical tag across them.
So in short: If you have a means to reduce the number of duplicates and redirect them - awesome. If you don't have a means to reduce duplicates, opening them up to Google is good, too.
For more information on making sure your canonical structure is set up properly, check out this Moz blog post: https://mza.bundledseo.com/blog/rel-confused-answers-to-your-rel-canonical-questions
