The case against (for most stores)
A well-built modern theme loads fast, ranks well, and lets your team edit everything without developers. Going headless means you now maintain a codebase, a hosting setup and a deploy pipeline; every content tweak that used to be a theme-editor click can become a developer ticket. If your reason for headless is 'performance', know that a clean theme hits excellent Core Web Vitals too. Most slow Shopify stores are slow because of app bloat, not Liquid.
When headless genuinely wins
Headless earns its keep when the storefront is really an application: logged-in member platforms with courses and communities, funnels with logic themes can't express, storefronts that mix commerce with rich interactive content, or brands running one frontend across Shopify plus other backends. I've built a membership platform with custom auth, affiliate programs and Klaviyo integration on Next.js; that product could not exist as a theme.
There's also a pragmatic middle path: keep the theme for the store, go headless for one experience (a funnel, a portal, a tool) that links back into Shopify checkout. You get the special experience without re-platforming everything.