Gestural scenarios envisage the emergence of language through conventionalisation of iconic gestures (e.g. Arbib 2012, Corballis 2003, Tomasello 2008). On these accounts, the starting point of the emerging language is the type of motoric-visual communication that is characterised by robust iconicity, spontaneity, non-normativity but also by open semantics (for review see Żywiczyński et al. 2018). I challenge the assumption – implicit in many of these accounts (most importantly, in Arbib 2012, Tomasello 2008 and Gardenfors 2018) – that the completely non-conventional system of communication is a feasible starting point for the process of language emergence. In doing so, I use the related phenomena of praxic and mimetic conventions (Zlatev 2015, including the literature on cultural transmission in non-human apes, e.g. Hicks et al. 2019) to show that even pantomimic enactments, which are considered by proponents of gestural scenarios as free from communicative conventions (for review see Zlatev et al. 2017), do contain minimal conventionality. Finally, I discuss the consequences of my critique for gestural scenarios, and explain how they would profit from the adoption of a dynamic conception of sign, conceived along the Peircean lines as the interplay between the iconic, indexical and conventional relations between content and expression (Peirce 1998, Jakobson 1965, Sonneson 2007, Ahlner & Zlatev 2010).