There is a read consistency problem, in that two sessions both running ...
insert into ... select max(..)+1 from ...
... at the same time both see the same value of max(...), hence they both try to insert the same new value.
You have the same problem with your table of maxima method, and you have to use a locking mechanism to avoid multiple session reading the same value. This leads to a concurrency problem where inserts to the table are serialised.