I think you misunderstood the end of the episode. The lesson Twilight learned is that she should not accept a task as demanding as babysitting when she already has so much to do (also, that when it comes to spending time, Quality>Quantity). Vice versa, Cadacne and Shining Armor learned that you shouldn't just spring such a huge responsibility with no prior warning. (Also, btw, the foals were not terminally ill. Terminally ill means that they can never be cured.)
I personally liked the episode. For one, I'm a sucker for cute babies, and Flurry Heart definitely falls under that. I also think that the lessen it taught was an important one, and applicable to not only babysitting: If you already have quite a lot to do, don't add other tasks onto your schedule, even if they are very, very fun to do.
The subplot of Cadance and Shining Armor at the Modern Art Exhibit was especially funny for me because I had just earlier that day a conversation about what 'art' entails. Perfect!