We consider the possible role of current large language models (LLMs) in the study of human linguistic cognition. We focus on the use of such models as proxies for theories of cognition that are relatively linguistically-neutral in their representations and learning but differ from current LLMs in key ways. We illustrate this potential use of LLMs as proxies for theories of cognition in the context of two kinds of questions: (a) whether the target theory accounts for the acquisition of a given pattern from a given corpus; and (b) whether the target theory makes a given typologically-attested pattern easier to acquire than another, typologically-unattested pattern. For each of the two questions we show, building on recent literature, how current LLMs can potentially be of help, but we note that at present this help is quite limited.