We could also put a big Play-The-Tutorial-Button in the main menu and have the tutorials automatically follow each other.

Personally, I would like tutorials to be unlocked one after another

Other thoughts:
If we look (for reference) at CR tutorials (as well as CE and CP since they didn't change very much) there are things that I liked there and thing that I did not:

First: Tutorials were put to the same hierarchy with all missions, settlement, races and so. (In fact I have contradictory attitude to the tree organisation of playable scenarious but these are mine problems alone). I suggest tutorials to be moved from this hierarchy (since people who have already passed them do not bother themselves from seeing tutorials folder again and again).
EDIT: Another thought. If moving tutorials out of the scenarios hierarchy they will certainly not be available during network play.

Second: (Tutorials didn't cover all the game aspects but they didn't have too). I liked how pieces of information were given one after another from tutorial to tutorial. Even though all 10 tutorial scenarious were available right away, I prefered to play them in sequence (even forcing myself to return to the one I failed to pass before moving to the next one).

Third: There is a good idea (as stated before) to have some "Play tutorials" button but after pressing it user should be taken to the screen where he/she can choose the tutorial to play (among the available ones).

Forth: Tutorial (as well as every other) progress should be saved to the current player profile (New profile will have only 1 unlocked tutorial to play). When moving to another PC user will have to move the .openclonk folder to the new place with all the progress achieved so far. If this directory is somehow lost, he/she would have to start all over again anyway.

Fifth (and the most important): No one forces you to play tutorials if you accidentialy lost your profile. Missions, Melees, Settlements will be available right from the start, so if you are already a Clonk guru, why don't you go there and play? :-)

In my opinion the cons outweigh the pros. If someone wants to try melee weapons before movement, that is his/her choice. Whether that choice is a wise one is rather irrelevant, most importantly not for us to judge about. And I think we can rely her on the fact that people can count from 1 to 10, and follow the sequence as intended if they want to.

P.S. Someone may have tried the first few toturials at a friend's computer and then wants to complete the sequence at home.

If you want to start tutorial 2 before playing tutorial one, show a dialogue:

"you serious about starting that already?! better play tut 1 bfore!"
[no NEVER] [omg youre so clever, i should do that]

If tutorials really are just tutorials, then yes, I think you should just allow an arbitrary order. If they get more adventure-like in the future, I would rather see them as a "learning campaign" and require progressive unlocking.

It should be left to players preference, everything else would be too restricting IMO. (With the same argument, you could allow players to play the real game only if they finished all tutorials. That would suck.)