Sure you can try out your game immediately in the editor, by pressing the play button - but can you edit Source code and it will be immediately applied without restarting and without losing the current game state?
You can edit and adjust scene objects in the inspector during play mode but those changes are usually thrown away after quitting play mode.
I never did serious mobile dev with unity but I same as above... updating and editing your game source persistently at runtime during playing doesn't seem possible, since it's completely compiling everything into an Android package right?
Building for all desktop platforms under a minute - this is 100% not true..... Almost all of the last hours of game jams where I used unity where spent in worry waiting for a long build process not being sure everything works all right afterwards - and that was always for just _one_ platform at a time...... DragonRuby builds your games into fully functional Windows, Mac, Linux, HTML5 and FWIW Raspberry Pi builds in under a minute in total for all those platforms. I don't know of any other Engine (except maybe LÖVE2D which is interpreted in its basic nature and doesn't need building) which can do anything close to that speed
Persistent flexibly modifiable game state? - maybe there's something in the asset store - but out of the box?
Cross-platform File storage is the only thing where I can see that that is probably a well solved problem in Unity....
I cannot speak for the other game engines. But in general it would be nice if you back up your claims.....