I guess I should keep my copies of the last three books on your list under lock and key. (Not to mention all three of the Curtis & Reiner books.) Sad to say, commercial publishers are not at all reliable about keeping advanced math books in print (especially at affordable prices). These books are not big moneymakers.

Characters only work well in characteristic 0, but their values lie in fairly small number fields. So you are not involved with the entire field of complex numbers. To work in characteristic p requires a real change of methods and usually a reformulation of the questions asked.

Concerning Brauer's proof, which uses standard character theory over fields of characteristic 0, the test for an element of a group to lie in the kernel of an arbitrary representation is that its character value should agree with the degree of the representation (the value of the character at 1). Here the given representation is faithful. The estimates here of character values rely on these being sums of roots of unity. I suppose Brauer wanted to emphasize the brevity of his proof, besides which he knew characters inside out.

There are two additional short proofs in Proc. AMS just after Curtis-Reiner first appeared, avoiding Burnside's use of complex numbers. (These back issues are to appear on the AMS journal page after scanning but haven't yet. I can access them through the UMass library or JSTOR, but these are restricted.) The two papers appear in the collected papers of the two authors: R. Steinberg, Complete sets of representations of algebras, Proc. Amer. Math. Soc. 13 (1962), 746-747 R. Brauer, A note on theorems of Burnside and Blichfeldt, Proc. Amer. Math. Soc. 15 (1964), 31-34

Yes, the component group permutes irreducible components of the Springer fiber, inducing a permutation rep on top cohomology. (This plays a nice role for subregular unipotents.) But the action in lower degrees is harder to study directly. And yes, some pairs do fail to occur. These are accounted for in Lusztig's generalized Springer correspondence. But it would be undesirable (for me) if all nontrivial characters of the component group failed to occur.

I really don't think of the older books as "classical", but instead as a response to particular needs at a particular time. The books emerged from a period in the late 1960s when many people wanted to assimilate and develop the ideas in the Chevalley classification seminar. Algebraic geometry at the time was very much in flux, with the approaches of Weil and Chevalley rapidly giving way. Borel's lectures at Columbia were written up by Bass and later turned into a sort of textbook by me, followed by Springer's and then an expanded book by Borel himself. All very ad hoc.

Geordie, the character St does occur (once) as a constituent of the DL character coming from the trivial character of any maximal torus. A quick reference is 7.6.6 in Carter's book, using the DL computation of inner products (as pointed out by Carter just after he defines "unipotent" characters in 12.1. I haven't traced this explicitly back to the DL paper or Lusztig's further development, but it's clearly a consequence of the earliest work on DL characters.

It's fun to make a wish list, but in real life it's hard to justify the cost of translating an advanced book for a limited market. It's always tricky to find a translator with the right mathematical as well as linguistic background, lacking which a reader may be better off struggling with the original book.

Two textbook references: (1) the detailed treatment of Gelfand-Graev characters in Chapter 8 of R.W. Carter, Finite Groups of Lie Type (Chapter 6 is about the Steinberg character); (2) the concise treatment in Chapter 14 of Digne-Michel, Representations of Finite Groups of Lie Type, where 14.39 defines "regular" character as a constituent of Gelfand-Graev and gives the Steinberg character as an explicit example. The general theory requires extra care if the ambient algebraic group has a disconnected center. (For me the term "generic" isn't at all helpful in this setting.)

There is one characteristic p situation in which representations like Steinberg (having maximum possible dimension) become generic in a geometric sense: consider all irreducible representations of the Lie algebra of a semisimple algebraic group, where those coming from the group ("restricted") such as the trivial representation are the least generic and where "most" representations have maximum dimension (p raised to the number of positive roots). But for finite or algebraic groups only the restricted ones are visible.