The study of ecological communities often involves detailed simulations of complex networks. But our empirical knowledge of these networks is typically incomplete, and the space of simulation models and parameters is vast, leaving room for uncertainty in theoretical predictions. Here, we show that a large fraction of this space of possibilities exhibits generic behaviors that are robust to modelling choices. We consider a wide array of model features, including interaction types and community structures, known to generate different dynamics for a few species. We combine these features in large simulated communities, and show that equilibrium diversity, functioning and stability can be predicted analytically using a random model parameterized by a few statistical properties of the community. We give an ecological interpretation of this "disordered" limit where structure fails to emerge from complexity. We also demonstrate that some well-studied interaction patterns remain relevant in large ecosystems, but their impact can be encapsulated in a minimal number of additional parameters. Our approach provides a powerful framework for predicting the outcomes of ecosystem assembly and quantifying the added value of more detailed models and measurements.