One of the benefits of booking a large "legacy" airline is that they usually have multiple options to get you from point A to point B. The smaller "ultra low-cost" airlines like Frontier tend to have far fewer options. They also don't have the customer service staffing levels that a company the size of Delta can offer.
As
sam_gordon notes, a schedule change (especially one where the connection is impossible) usually means you have carte blanche to choose any other flights. As long as it's the same class of service (i.e. coach), the change should be free.
For anyone finding themselves in this situation,
kaytieeldr's suggestion about finding your preferred flights before calling is a great one. If the agent doesn't have to spend time searching, that makes their job easier. As someone who used to work in a travel call center, I loved it when a guest called with a problem and provided a requested solution to that problem.
edit to add: they didn't even notify me of the change, I just happened to log on to my account and saw it. I wonder why?
Typically, airlines make schedules changes on Saturday nights. Any guest that is affected by a change will be notified of the change. However, that notification might not be immediate. Notifications happen based on the flight date. If your flight isn't in the next week, you might not get notified until Monday or Tuesday.
According to Wikipedia, Delta operates 5,400 flights every day. That's 1,971,000 flights annually. If just 0.5% of those flights have a schedule change, that's 9,855 flights. If you assume there are 150 people booked on each of those flights, that means Delta has to notify 1,478,250 people. As great as technology is, it still takes time to process that many emails.
(Note: While the total flights is factual, the rest of those figures are arbitrary. I don't know what percentage of flights are usually changed nor do I know the average number of people booked on those flights.)