As others have said, this sort of thing has been done before with varying degrees of success. Before 1960 or so it was very common for people to do almost nothing but intervals. I'm not going to do this, but somewhere online, maybe even here, someone put a copy of Fred Wilt's "How They Train; One to Six Miles." If you can find it you'll see a lot of samples of people who trained that way. I trained that way in my early years.
So much of that changed with Lydiard I think for the most part because his approach was more successful than the "nearly all intervals all the time approach." Schul's Olympic gold was one of the last hurrah's for that approach. Tracy Smith made the US Olympic team in 1968 training mostly on intervals. Mark Covert had a pretty good college career and got close to making the '72 Olympics in the marathon on an interval heavy approach. But I think as time went on most people found that they ran faster and enjoyed training more by doing steady runs with some interval work in the mix.
A big problem I see with interval work is that it's very tempting to turn every session into a race. You're timing nearly everything and it's discouraging when you're getting splits that aren't as fast as they were the last time you did this session so you push yourself a little harder to get the times you want. But I do think if you really understand training principles you should be able to put together a successful program where you're doing almost nothing but interval sessions.