The problem is that leaves you with an unstable situation under FPTP. Let's say that our fictional third party, the Yellow Party, is to the point where 40% goes to Republicans (right), 30% goes to Democrats (center-left), and 30% goes to Yellows (left). Now Republicans are winning despite Democrats and Yellows forming a majority. So Democrats are going to split at some point, arriving back at an equilibrium of approximately a 50-50 split between Republican-Democrats and Democrat-Yellows. So in essence, you're right back where you started.