It depends on the God and the avatar in question. Rama is seen as the ideal man. For women that means the kind of man they desire and commit to. Devotion to Krishna too is flirtatious. Radha is revered for her devotion to Krishna, but their love may have been chaste but was romantic. Shiva is often seen as the epitome of masculinity and virility. It would be very creepy to have the same Gods who are seen as "desirable" to also become "'father-figures."
Goddesses, on the other hand, are subject to the Madonna-whore dichotomy. A man can be seen as both desirable and worthy of devotion. Women on the other hand are either mothers/wives/sisters, if they become the subject of desire they are whores. Mortal women could bear the children of God's but mortal men desiring Godesses meet bitter ends. This isn't true just in Indian mythology, but in most mythologies.
Barring Aphrodite/Venus, most Goddesses are treated as mothers and wives of other Gods and not looked upon with desire. IMHO, its deep-rooted patriarchy that has been around since ancient times.