The problem with that is one of social momentum. The Republicans and Democrats are already huge and established. A party starting out will be tiny and have no hope of winning, so the people who might be peel-able will see it as "wasting their vote." Which means the party really won't grow and ever reach that critical mass. It's like that old saw "Need experience to get a job, need a job to get experience." You need to attract voters to win, you need to win to attract voters.
I mean, we've seen this. Theoretically, the libertarians should be able to peel from both parties--on the classic, overly-simplified axis of conservative vs. liberal, libertarian policies are conservative for some things (financial, largely) and liberal on others (social). But the Libertarian Party has really not been able to grow at all. Sometimes they do a little better or a little worse, but there's no upward trend.