The European Open Science Cloud (EOSC) is envisioned as a transformative platform for advancing Open Science, aimed at benefiting a diverse array of stakeholders, including researchers, innovators, institutions, and the broader public. To fully harness EOSC's potential as a common good, capable of delivering services to the research community such to potentially transform the way scientific production and communication is done, we address critical barriers that may actually restrict the equitable access and the optimal use of such services. In particular, we emphasize that key resources as required to access and exploit EOSC's advanced FAIR-data services - such as data-processing algorithms - are, in fact, intrinsically limited and the access will be competitive. Governance and funding of EOSC present challenges associated with its effective openness in terms of accessibility to resources for its advanced exploitation.