To begin to answer your 'abstract question', "What are Silver Machines good for', one need only look at the title of Prof. Silver's unpublished manuscript

>"How to eliminate the fine structure from the work of jensen"

to find the beginning of the answer.


Why does one wish to eliminate the fine structure of Jensen?  For the reason given by Boris Piwinger in section 0 of his Diploma Thesis found by clicking on the link "Silver Machines" found in Prof. Golshani's answer (I am quoting from an English translation I found on the Web--on pp. 2-3 of the translation):

>The idea [of fine structure theory--my comment] is to have a closer look at the passage from $L_{\alpha}$ to $L_{\alpha + 1}$ and to describe the process with some "bookkeeping device".  Even today--after 25 years of development--, this method is extremely complicated and wearisome [is it really?--my question].


This is the correct context in which to frame the OP's question (at least in my opinion). 


Addendum:  I also find the following passage found on pg.3 of Piwinger's Thesis of interest and relevance here:

>Also in the early seventies, Jack Silver found a different approach--the Silver machines.  These machines reduce the considerations to calculations on sets of ordinals.

This leads me to wonder whether Silver machines can be considered as a type of Ordinal Turing Machine (OTM) and by the following theorem

>A set $x$ of ordinals is ordinal computable form a finite set of ordinal parameters if and only if it is an element of the constructible universe $L$.

one can reduce the primitive recursive set functions of Jensen and the Silver machines to this seemingly irreducible form (OTM's).  This would serve to eliminate (hopefully) the concern regarding the "reformulating the salient properties of the (Jensen) hierarchy" Prof. Eisworth has regarding the Silver machines (though reformulating to simplify is certainly an important gain) and perhaps provide a means of classifying the various Fine Structure Hierarches as particular classes of OTM's