Why is the E2 protein important for protein degradation?
Pretty hard question, "why", as we've not been watching for the millions of years it took to build that system... I think the better way to look at it is to name the advantages this system has and hypothesize on it's selection. BTW in biology a good answer to why is always because.

I would guess though that given the function of ligases, it has been selected against due most probably to lack of selectivity. E1s are very small and already need to do both activation of Ub consumming atp and doing a somewhat major conformation shift to accept ligation of the activated Ub. The amount of Protein Protein surface usually required to maintain the exquisite selectivity that is required for such a system can be assumed to be too great for the size of the E1s. 

Then if you ask why it did not evolve in some kind of huge multidomain protein; I would probably argue to the point that you need to produce a very large amount of it all the time, and that it must be somewhat difficult to target that protein for proteosomal degradation / make sure it's folded properly. Having a smaller footprint might help in keeping the domains ordered and reducing entropy hence making sure the protein stays functionnal longer.

Then why not the E2 doing it directly, and why do you need the E3 in between... Well again, I would assume this is also a question of selectivity. If you need to regulate thousands of cytosolic proteins and control their regulators at the same time, you need some modularity, you need the ablity to create multi protein complexes that bring different layers of regulation and cannot assume that one protein can do that. The term E3 is also some horrible bin where people put anything. E3 are very often large and sometime huge multiprotein complexes, think of the APC complex, or in the most well documented cases, the Cullin complexes. 

The way E3s evolved is pretty cool actually, to recruit E2-Ub a protein just needs to get a domain through some mutation (RING, U-Box, HECT...) then it can target whatever it used to bind to a degradation complex. That is some pretty neat and quick trick to create diversity rapidly if a system actually does something that brings an evolutionary advantage. 

I see you left out the E4 which may play a role in Ub chain propagation but as they pretty much function as E3 anyways, there is debate as to why we would need to use that terminology.

This is by no mean some definite answer since I could be wrong on most of these things. I hope I helped you to further your reflection on the subject.