It's not that learning the Italian language at home isn't going to work or is just plain silly but traveling to where the language actually originated is a double plus. It is still an unbeatable way to acquire a second language. Just imagine yourself in the midst of the historical places that you usually read only from books. Take for example the famous ruins of the Colosseum is just an amazing site to see and be in. There is nothing like the experience of being in the location where a lot of history had occurred over the time.
But what is really the big hype in traveling and living to the Italian speaking country? Although the expenses are not to be questioned (because it's obviously an important part of immersion and travel); the natural way of learning and speaking the language comes to you just like how your dog obeys every word you tell him. The best part of learning a new language, as they say, is when you don't force any information in to your mind. When necessary information from an important subject enters your mind freely but with your full interest focused to it; you learn the most natural way.
Indeed getting to know a language doesn't come easily. It takes time and initiative. But for any person who strives hard to learn, it doesn't have to take more than the actual process required itself. As a beginner, you'll realize that the more you appreciate the lesson and practice it to your everyday life, the more it becomes a part of your self. Even when you don't see yourself in an immersing in Italy for the language, try your best to immerse with all Italian sources you can reach right from your own home.