Some languages constrain the recursive embedding of NPs to some specific morphosyntactic types, allowing it for example only with genitives but not with bare juxtaposition. In Indo-European, every type of NP embedding — genitives, adjectivizers, adpositions, head marking, or juxtaposition — is unavailable for syntactic recursion in at least one attested language. In addition, attested pathways of change show that NP types that allow recursion can emerge and disappear in less than 1000 years. This wide-ranging synchronic diversity and its high diachronic dynamics raises the possibility that at many hypothetical times in the history of the family recursive NP embedding could have been lost for all types simultaneously, parallel to what has occasionally been observed elsewhere (Everett 2005, Evans & Levinson 2009). Performing Bayesian phylogenetic analyses on a sample of 55 languages from all branches of Indo-European, we show however that it is extremely unlikely for such a complete loss to ever have occurred. When one or more morphosyntactic types become unavailable for syntactic recursion in an NP, an unconstrained alternative type is very likely to develop in the same language. This suggests that, while diachronic pathways away from NP recursion clearly exist, there is a tendency – perhaps a universal one – to maintain or develop syntactic recursion in NPs. A likely explanation for this evolutionary bias is that recursively embedded phrases are not just an option that languages have (Fitch et al. 2005), but that they are in fact preferred by our processing system.