Why is the Hubbard model written down so late? It is just the tight binding model plus on-site interaction. 
What prevented people from arriving at the Hubbard model?
 A: Well, when did you want it to be written down?
As it is, it was pretty much simultaneously and independently arrived at by Hubbard, Kanamori, and Gutzwiller an awful long time ago. Probably others too. The point is, it was written down when there were experimental phenomena that justified including interactions in the model. It wasn't some great conceptual or technical coup, it was just a useful model of electron behaviour in narrow-band materials, which weren't really a major research topic before the 1950s.
A: min Zhang,
The Hubbard model (offen reffered to as the U and J terms in ab-initio DFT or tight-binding models) is a little bit more complicated than it looked like. 
It is indeed an additional energy that you add locally to some states (d or f bands usually) to locallized them. Usually you want to do this because DFT tends to spouriously delocallize electrons. 
The problem is that by adding this term you were, among other problems, breaking the symmetry of your crystal. 
They had to develop full rotationally invariant fomulation of the term to make it usable in practice. See for example:  
A.I. Lichtenstein, V.I. Anisimov and J. Zaanen PRB 52, 5467 (1995) 
Sam
