Can Batman and Catwoman / Elektra be friends (and perhaps even lovers)?

Would it possible for Batman and Catwoman to just love each other instead of trying to kill each other? Is there a REASON these two fine people MUST be enemies and not friends (and perhaps more than friends) and work together for good?

Same question for Batman and Elektra. MUST these two superior beings remain enemies, or is there a chance, in a reasonable universe, that they could become friends and perhaps work together and, well, play together?

Where in the world is the battle? I can't see it!