[quote author="Scott S."]In the first schem you could take the feedback from the output side of C3 and eliminate C2, it will work fine.[/quote]
Hi Scott, and welcome to the Lab. What you describe will work fine if the load is known, fixed and non-reactive. If the load varies, or is reactive, then the frequency and phase shift characteristics of the feedback loop become variable, which is generally not a good thing. (On the other hand, it is common to include a reactive component--the output transformer--in the feedback loop in power amp designs, but the designer is usually working with a particular transformer, with known characteristics, in mind).
As drawn, the 1uF coupling cap and 100K feedback resistor are flat in the audio band; but like you say, you could use a smaller coupling cap to reduce the feedback at low frequencies and give the amplifier a low-frequency rise. One must be careful of excessive phase shift, of course. Even though it's kinda "cheating", stuff like that is sometimes done to compensate for, say, a cheap input transformer with poor bass response. And of course, it's normal practice in equalized amplifiers such as RIAA preamps.