Jesus didn't teach us to ask God persistently in order to wear God down until He gives us everything we want. Instead, Jesus wanted us to learn that persistence in praying teaches us to wait on God, not to change His mind. This helps prepare us to receive the answer God knows is best for us. Prayer does not enable us to make unreasonable requests of God. We need to trust Him and continue persistently with prayers that are appropriate for our needs and respectful of the Father.
Most parents are willing to provide for their children's needs in love.
This illustration Jesus gave teaches us about God's willingness to answer His people's prayers. Yes, there are some earthly fathers who do not provide well for their children, nor do it in a loving manner. But God, our loving heavenly Father, loves us perfectly. If we, as earthly parents, know how to give good gifts to our children, how much more does God know how to give good gifts to us when we ask. In fact, His most wonderful gift to us is His constant presence, the Holy Spirit.