Jack Campin I much prefer "anyone can jump in" to "everyone gets their turn in sequence" - taking turns leads to people abusing their slot to waste time shuffling through books or tuning, which loses all the energy and momentum that may have developed. If you can't be off and playing in ten seconds, pass.
I don't see that at the sessions I go to. There are 3 that I attend when I can, in Kent, Sussex and Devon. All operate "roughly" on a sequence basis ( but a couple of them have the strict sequences punctuated sometimes by one or other of the "mainstay" attendees leading off on a tune or song for all to join in). No-one faffs with books or tuning at any of them....if you're not quick to start when your turn comes around, as per your last sentence, the opportunity passes on.