Neo
In most tune sessions everyone who wants to has the opportunity to lead a tune or set of tunes. More so in the more informal spontaneous gatherings. When the current tune stops, you just start.
In the sessions that have 'leaders', it can be more of a problem but lot of players are quite happy not to start a tune and are happy just to play along. Sessions are more of a collective effort than one of personal glory
Songs are not usually done at these sessions because all the musicians can do is 'twiddle their thumbs', whilst the song is in progress.