Vertical AI firms in accounting, law, healthcare, procurement, and similar domains historically bundled workflow, domain logic, and accountability into a single application. General-purpose AI agents are now unbundling that package, prompting founders and investors to advocate "going headless": cede the workflow and interface to agents and expose domain expertise as callable services. This article argues that going headless is correct for some firms and destructive for others, and that the latter often cede their value capture inadvertently through architectural choices that look like interface decisions. This is a boundary question, and the answer turns on distinguishing the interface boundary, which can often move, from the accountability boundary, which often must not. Drawing on Coase's theory of the firm, Eisenmann, Parker, and Van Alstyne's platform envelopment framework, and Teece's analysis of complementary assets and appropriability, the article shows that orchestrators operating through open protocols acquire envelopment power even as technical interoperability improves, and that durable value capture concentrates in cospecialized accountability assets: professional signoff, regulated workflows, evidence trails, and trusted systems of record. The article proposes a three-position taxonomy (component, integrated software platform, dual-track) determined not by sector but by task-accountability regime, and formalizes the construct of rule debt: the future governance, maintenance, and accountability burden that accrues to customer organizations when business rules and professional standards migrate from governed systems into prompts and agent instructions. Four principles follow: decompose by accountability not interface, invert the edges while retaining the core, position rule debt as the customer cost the integrated platform prevents, and avoid single-orchestrator dependence.