Yes, it is safe to assume that all search engines want your XML Sitemaps to be as clean and accurate as possible.
XML Sitemaps give you an opportunity to tell search engines about your most important pages, and you want to take advantage of this opportunity.
Think about it another way. Let's pretend your site and Google are both real people. In that hypothetical world, Google's first impression of your site is established through your site's XML Sitemaps. If those Sitemaps are full of broken links, redirecting URLs, and rel="canonical" pages, your site has already made a bad first impression ("If this site can't maintain an up-to-date Sitemap, I'm terrified of what I'll find once I get to the actual pages").
On the other hand, if your XML Sitemaps are full of live links that point to your site's most important pages, Google will have a positive first impression and continue on with the relationship