I haven't worked w/ arena_lib a lot so far but from what I've learned by going through the documentation and fixing some bugs of existing minigames, I think it seems quite powerful. What is especially interesting is the editor mode where you can edit arenas with special "items" in your hotbar which act like some kind of "mini menu". It is unusual but I understood it somehow.
Nothing of the mod's design seems to disturb me so far, coding with it is fairly reasonable with no weird surprises.
A minor downside are the signs because they introduce non-translatable text. Signs are hardcoded in arena_lib and can't be removed but I've read it is possible to add alternative entry methods (not tested so far).
The only major criticism I currently have is that there is no player or admin manual, only a programmer's manual because not everything is obvious from the player/admin perspective (although it is mostly intuitive already). For example, I don't know how many players are aware that you can rightclick the signs to enter spectator mode. And it also took me quite some time to figure out how to set up my own test world with arena minigames because the documentation doesn't say.
Arena_lib has been successfully supporting the A.E.S. minigame server which is I guess evidence enough for it's power. Overall, I can give it a clear recommend.
About the admin manual: a few days ago I edited the README saying to do /arenas help to learn how the mod works, so I think that part is covered. Having the in-game guide allows me to translate every instruction, something I can't do in a separate .txt/.md/etc file, so I think it's a better solution (I expect modders to have a good English level, but it's not always true for server admins).
About the player manual, I don't think it's something arena_lib should do. I cannot know how someone is gonna configure their servers, so I can't force aspects like an instruction formspec on players' first login. I could open a formspec the first time they hit a sign, but with this logic how are they gonna know about hitting the sign in the first place? What I'm saying is, it's something that is up to the server admin. Also because players aren't gonna check the arena_lib folder. For instance, on A.E.S. we have a custom mod opening a formspec the first time you log in. Other servers might opt for a different solution, like placing a couple signs before the minigame area, explaining how arena signs work.
About translations: that's not arena_lib's fault, as signs_lib (the dependency that brings arena signs to life) use entities to show the text. The optimal solution would be Minetest adopting text on nodes (there is also a bounty): https://github.com/minetest/minetest/issues/1367