As someone who never ever thought travel insurance was worth it...I have come to change my mind.
In today's market every airline is cutting back on "goodwill" gestures. The speed and degree to which Delta will respond is directly proportional to how valuable you are to them as a customer. They will respond - but when the weather is miserable and the headaches are many - the response will take some time. In fairness, your complaint is not as urgent as the complaint of the passenger stuck between flights today.
I was talked into buying insurance on a trip a last year. That was the first time I had ever done that. It wasn't expensive and the coverage was far better than I expected. I'm sure there are good companies and bad ones but there was a website called insuremytrip that helped me sort through the options and even though Delta tends to respond very quickly when I have an issue I've decided that the value of my time is such that travel insurance is no longer a waste of money.