You curent query has 3 independent MAX() functions. That is, while
every values RELNUM, RELSPEC and EDIZ was coming ultimately in query
below the row (AGGNAME, RELNUM, RELSPEC, EDIZ) may not exist.
To answer the request:
"Give me the rows AGG_NAME for which AGG_RELNUM, .. is maximum!"
you need OLAP:
SELECT AGGNAME, AGG_RELNUM, AGG_RELSPEC, ED
  FROM
  (SELECT ROW_NUMBER()
           OVER(PARTITION BY AGGNAME
                    ORDER BY AGG_RELNUM DESC, AGG_RELSPEC DESC, ED
DESC) AS rn,
           AGG_NAME, AGG_RELNUM, AGG_RELSPEC, ED
      FROM (....) AS T) AS S
  WHERE rn = 1;

(you can add/remove elements to the PARTITIONIN BY and the ORDER BY
clause as required for your semantics.

Yes, absolutely