Are you really that ignorant and incapable of noticeing basic abilities of people?
Current manga logic. Star pupil(genius of a generation) of Jiraiya(who has sage mode) has sage mode. Son of said pupil learns sage mode.
All of these people had TOAD contracts previously. Thus they were able to be reversed summoned for training of sage mode.
None of nagato, konan nor yahiko had a toad summon. As such they were incapable of being reversed summoned, and taught sage mode.
There is nothing illogical, or wrong with kishis logic, that would make it make sense that nagato would know sage mode.
Sure it is questionable, as to WHY now of all times minato is useing sage mode. Or to why oda had him use it just to get fodderized. But it was perfectly logical for minato to have sage mode.
As I would not like to just be negative in this post, I will say something positive that both you and me agree on.
Darth Bane was a boss.