A humble petition for changes in the MP unit roster of EB 2

[Ludens]

Maybe, but at the same time the legionary cohort is a unit capable of "solo" operation and I think that their unit size reflects that...

That would also mean legionary cohorts should have more men than phalangite units .

I don't see a warrior as someone who lives by waging war, because actually he spend more time working as trader or farmer, while the soldier doesn't do anything else during his career...

I understand you want to make a distinction between professionals and part-time fighters, but "warrior" is not the right word. Professional soldiers are sometimes called warriors. And consider the etymology of the word: why should the term warrior be applied to levies but not those who make their living from war?

The warrior is more concern in loot and fame...

Those people who are farmers (traders, artisans, craftsmen...) first and fighters second do not go to battle for loot. They are mostly there to protect their homeland. It's the soldiers and the warrior castes that care most about fame and the spoils of war, because warfare is what they owe their status to (and because the pay of the rank-and-file has always stunk).

The young poorly-trained levy start with no experience and fight in single combat, if he survives become more expert and maybe richer...
Yes, they form some sort of formation, but in detail everyone is fighting his own duel, while soldiers are more packed and fight in cooperation...

What you describe is correct for skirmisher levies, but I doubt that close-order levies, such as hoplites and lugoae, would abandon their formation and engage in a series of duels. Rather, they would do what frightened men of all times have done and stand closely together. The resultant wall of shields would have offered them more protection. Yes, their formations would have been simple and there would have been no "squad tactics", but it definitely wasn't a series of duels.