who is he
I don't think it'd be too different if they hit eachother hard tbh.
By that logic, Fighting would be super-effective against everything, and I don't think I need to point out the problems that would cause.
Also, if you were to throw a boulder at someone at full power that would probably be considered "super-effective" too, if being "punched hard in the face" were to be. So Rock would be super-effective against everything, too. Or at least against Psychic, since you seem to think that Psychics are not very beefy by nature (although Reuniclus would beg to differ).
I can totally understand why, in your example with frail Alakazam, you would think that Fighting-type attacks should be super-effective. But as stated above, all type advantages/disadvantages can be argued. Because of that, limits need to be in place, or else everything would be super-effective against everything else. Also, as also stated above, not all Psychic-types are frail, and some actually have good reason for being able to resist such attacks.