Have you read the Punisher Max series? Most of the guys he kills are not petty criminals who are guilty of low level robbery or drug offenses, he kills psychopathic monsters guilty of some of the worst crimes you can imagine. Here is a good list of some of the worst criminals the Punisher has faced:
http://tvtropes.org/pmwiki/pmwiki.php/Monster/ThePunisher
In Max he fought a gangster who murdered his own family and tricked a rival crime boss into eating his own son. Frank also fought human traffickers who traded in sex slaves and raped them to break their will. Those people are not going to be rehabilitated, they are vile psychopath who will continue to victimized other people. I actually prefer those stories to stories where Punisher is merely a foil for DD or Spidey, Punisher killing evil scum bags is interesting in my opinion because it does challenge the audience. What Punisher does is clearly illegal and immoral, but put him against an evil psychopath and you might root for the Punisher despite that. Really how sympathetic Punisher is depends on who he is facing. Sure DD is more sympathetic then Frank, but Frank is more sympathetic then the criminals he fights.
I think a lot of people would would think criminals who are guilty of such heinious crimes do deserve death. That is the moral ambiguity with Punsiher, his methods are wrong, but going after such nasty criminals makes him sympathetic.
Anyway, I think while Frank is a DD antagonist when they face off, he is not Big Bad material, you need someone for Punisher and DD to fight against. Punisher likely wouldn't go out of his way to kill DD, he would be more interested in killing criminals and would want DD to help or stay out of his way. Putting Punisher and DD against the same villain, using different methods, makes for a better way to contrast their methods more then anything else would.
I would disagree with that, there is a big difference between Punisher and most of the psychos he fights. Punisher is not a boy scout, but he morally superior to a slaver or a gangster who murders his own family.