They are really country specific. Bear with me. There are success stories and there are failures in postal banking across Europe and in Asia. Those that have been established for many decades are significant aggregators of deposits such as in Japan and Italy, which was an underserved market where the post bank has been in existence for quite some time; in others, a post bank launched in 2007 was closed in 2010.
In Brazil, it's a significant bank, but it's a money-loser. By and large, the post banks that have been most successful have been subsidized where they have been in existence for decades.