You're thinking about this in not really the right way.
When we parallel words, we want to make sure it's obvious they're connected. This might be because they're part of a list, or because they're part of a paired phrase.
In your first example, we make it obvious the words are connected by not repeating the word "to". The reader notices that "spark" and "motivate" are lacking "to", and concludes that the words are all part of a list.
What would happen if we skipped repeating "to" in the second example?
"We would like not only to hear your side of the story but also provide a response."
Now it's not clear that provide is supposed to be parallel with hear and that they're paired. Provide might be paired with like, even.
Do you see what I mean?