Is just requesting every URL enough to warm the cache?

You can check whether it actually worked by looking at the response headers on a real visit. Cloudflare sends cf-cache-status (HIT or MISS), and most other CDNs and caching plugins add something similar. Also logged-in users and anyone with a cart cookie usually skip the cache entirely, so test logged out.

It warms something, just maybe not the thing your visitors hit. The usual gaps: 1. CDNs cache per edge location. A crawl from your server warms the one or two PoPs nearest to it, and users on the other side of the world still get a miss. 2. The cache key usually includes more than the URL. If you vary on device, Accept-Encoding, a cookie or query strings, a plain curl only fills one variant. Send the same headers a real browser sends, and do a mobile pass if you serve a mobile variant. 3. TTL. If entries expire after an hour and the crawl takes two, the start of the site is cold again by the time you finish. For a page cache on the origin (WordPress plugin, Varnish, that kind of thing) requesting every URL with browser-like headers is mostly enough. For a CDN I'd only warm the top pages and leave the rest to traffic.