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Mike, you write ``it is very easy to carry out computations ...''. Of course, Mackey functors only apply when you are in an RO(G)-graded context. But that is a detail. As you know, you lucked out in the Kervaire invariant one problem and only needed "easy'' computations. To avoid giving a wrong impression, people should be warned that in fact there are relatively few fully worked computations, and even things like rational equivariant characteristic classes in Bredon cohomology are still unknown. This is an area in desperate need of hard work, even for cyclic groups of prime order.
Think about what $\Omega^{\infty}$ would mean in the simplicial world. There are serious advantages to being eclectic. For a different, Segalic answer to your original question see Mandell, May, Schwede, Shipley ``Model categories of diagram spectra'', especially \S 18.
