Real-world social networks often exhibit high levels of clustering, positive degree assortativity, short average path lengths (small-world property) and right-skewed but rarely power law degree distributions. On the other hand homophily, defined as the propensity of similar agents to connect to each other, is one of the most fundamental social processes observed in many human and animal societies. In this paper we examine the extent to which homophily is sufficient to produce the typical structural properties of social networks. To do so, we conduct a simulation study based on the Social Distance Attachment (SDA) model, a particular kind of Random Geometric Graph (RGG), in which nodes are embedded in a social space and connection probabilities depend functionally on distances between nodes. We derive the form of the model from first principles based on existing analytical results and argue that the mathematical construction of RGGs corresponds directly to the homophily principle, so they provide a good model for it. We find that homophily, especially when combined with a random edge rewiring, is sufficient to reproduce many of the characteristic features of social networks. Additionally, we devise a hybrid model combining SDA with the configuration model that allows generating homophilic networks with arbitrary degree sequences and we use it to study interactions of homophily with processes imposing constraints on degree distributions. We show that the effects of homophily on clustering are robust with respect to distribution constraints, while degree assortativity can be highly dependent on the particular kind of enforced degree sequence.