Python - problema (modulo random) con funciones def

]

#Ejemplo exitoso:

print(user_id_gen_by_user()) # user input: 5 5

#output:

#kcsy2

#SMFYb

#bWmeq

#ZXOYh

#2Rgxf

#Intento fallido

import random

#Carácteres que contendrán cada id

chars = 'abcdefghijklmnopqrstuvwxyz1234567890'

char_list = []

char_list[:0] = chars

#Función no exitosa de la que quiero ver el fallo

def user_id_gen_by_user():

    charsize = int(input("Enter Character Size: "))

    charlimit = int(input("Enter how many user ids to generate: "))

    for _ in range(charlimit):

        for _ in range(charsize):

            identity = "".join(random.choice(char_list))

            return identity

def user_id_gen_by_user():

    charsize = int(input("Enter Character Size: "))

    charlimit = int(input("Enter how many user ids to generate: "))

    identity = ""

    for _ in range(charlimit):

        for _ in range(charsize):

            identity += random.choice(chars)

        identity += "\n"

    return identity