I found a web page that explains how to find the gaps in a sequence, yet I want to understand why nextval() doesn't begin with the max(FK)+1 value.
For efficiency the only thing used to determine the next value of a sequence is the stored value of the last sequence value issued. Where that value may have been used, in a table as a PK or some other purpose, does not enter into it. Using a sequence as a default does indeed become problematic if you don't use it exclusively. If you do use it exclusively usually you just set the last value to be the maximum needed and use it going forward. The numbers from deleted rows simply remain missing in the table.