It's not hard to prove that local NFB works better:

Consider an amplifier with a given gain-bandwidth product. It might be a perfect integrator (i.e., infinite DC gain, dropping to 1 at some frequency), or it might have finite low-pass gain. Op-amps are reasonable integrators in the audio band, thanks to the prevalence of dominant-pole compensation. The typical op-amp has a gain of perhaps 100dB (i.e., 10^5) at DC-50Hz, then drops at -20dB/decade until fT is reached at 50Hz * 10^5 = 5MHz.

With a feedback loop, you can divide the GBW however you want. If you want at least 50kHz bandwidth, you can get only 5MHz/50kHz = 100 gain.

If you chain two such amplifiers, you get twice the gain (i.e., 200dB at DC), and the same fT, but twice the phase shift. You can't even put NFB around this loop, it will oscillate (in principle, at *any* frequency)! The only useful range for this amplifier is before the cutoff frequency (i.e., 50Hz), because the phase shift is low there. If you apply enough NFB and compensation so that gain < 1 before phase shift hits 180 degrees (which is somewhere past cutoff, since the angle is exactly 90 degrees at cutoff, which is still okay), you can get it stabilized, but now your bandwidth is clearly so much less than expected.

This serves as an extreme example: chained stages, transinfinite gain and monstrous phase shifts are not useful, but you already knew that.

If, instead, you use local feedback around each amplifier, you get a series of amplifiers, each with moderate gain, and zero phase shift through the passband. The phase shift increases substantially past the passband, so you can still apply dominant-pole compensation to this system as long as gain drops below 1 at that point. For example, if you wanted 100kHz bandwidth, you can still get 2500 gain from two op-amps (each stage wired for 50), which is almost as much as you get from a single mediocre op-amp.

If you go with a *lot* of stages, you get a serious amount of phase shift at the end, at cutoff, making global feedback more difficult. This compromises the overall system bandwidth. Fortunately, the dominant element in a tube amp is always the output transformer, so you're looking at accommodating that, and driving it without causing distortion.

Note that the analysis works on both ends. If you have a bunch of stages with coupling capacitors, the phase shift and LF cutoffs will add up! This makes the Williamson topology rather comical: it seems to have been intentionally designed as a power phase-shift oscillator!

Tim