If many mutations confer no immediate selective advantage, they can pave the way for the discovery of fitter phenotypes and their subsequent positive selection. Understanding the reach of neutral evolution is therefore a key problem linking diversity, robustness and evolvability at the molecular scale. While this process is usually described as a random walk in sequence space with clock-like regularity, new effects can arise in large microbial or viral populations where new mutants arise before old ones can fix. Here I show that the clonal interference of neutral variants shuts off the access to neutral ridges and thus induces localization within the robust cores of neutral networks. As a result, larger populations can be less effective at exploring sequence space than smaller ones—a counterintuitive limitation to evolvability which invalidates analogies between evolution and percolation. I illustrate these effects by revisiting Maynard Smith's word-game model of protein evolution. Interestingly, the phenomenon of neutral interference connects evolutionary dynamics to a Markov process known in network science as the maximal-entropy random walk; its special properties imply that, when many neutral variants interfere in a population, evolution chooses mutational paths—not individual mutations—uniformly at random.