Online platforms have disrupted parts of the capitalist economy, but assessing the magnitude of this effect is difficult. Much is known about major platforms, but less about the conditions under which they take over—or fail to take over—a given market. Unlike explanations emphasising slow take-up by entrepreneurs or worker resistance, we argue that historical and organisational characteristics of markets make them resistant to the platform model. In Germany and the UK, intermediaries have digitalised to varying degrees. Three market characteristics have combined to limit ‘platformisation’: (1) irreducibly qualitative assessments of value; (2) the complexity and contingencies inherent in the task that resist unbundling (3) fragmentation of the organisational field. Hence we show how the dynamics of work in live music limit the traction of the platform model. However, partial and hybrid forms of digitalisation still contribute towards intensified discipline over live music workers, threatening pay and working conditions.