Negative feedback is the right choice for the vast majority of amps, particularly direct-coupled solid-state, where you can pile on the gain and use that "excess gain" to minimize distortion via feedback. To oversimplify, if you have 20 dB (a 10:1 voltage ratio) of excess gain, you can have 20 dB of feedback, which will reduce the distortion in direct proportion to the feedback ratio ... in this case, ten times. Pretty slick trick.
In practice, as the excess gain goes up, and the feedback ratio increases, problems with stability creep in. Marginal problems with stability result in overshoots on square waves, and as it gets worse, brief periods of near-oscillation, and then full-power oscillation, which usually destroys the speaker. So you have to take account of the total phase shift on both ends of the spectrum, which includes the output transformer if it is included in the feedback loop. The phase shift of an output transformer typically limits tube amp feedback to no more than 20 dB, but this can be evaded by having multiple nested loops, as in the Citation amplifier deigned by Stu Hegeman in the early Sixties.
But now we get into the (much) deeper waters of both slew-rate limiting and settling time, which are interrelated. That’s beyond the scope of this discussion, but they are limiting factors in any feedback amplifier. Multiple feedback designs can achieve impressively low distortion figures, but settling times can be much longer, since each nested feedback network has to leave saturation, return to controlled operation, and return to zero with its own time constant.
These are not trivial design concerns, and made more complex by load dependence ... a reactive loudspeaker load will decrease the phase margin of the amplifier, and that in turn leads to longer settling times. As the phase margin erodes, settling times get longer and longer, until the amplifier breaks into self-oscillation.
The other consequence of loss of phase margin is an increase in distortion, mostly at high frequencies, with the limit case of oscillation, which can be considered 100% distortion, with the output effectively decoupled from the input.
For obvious reasons, great care is taken in the design phase to avoid oscillation, but there are amplifiers where stability is conditional on the load, with transient overshoots visible under some conditions of load and input stimulus. This was a serious problem with first and second-generation transistor amplifiers. (Which were designed with nothing more than slide rules and nomograms, so you can’t really blame the designers back then.) Nowadays, software modeling programs allow designers to avoid the stability problems of the early transistor amplifiers.
If you want to jump down into the rabbit hole, read about "Nyquist Stability Criterion", followed by "Slew Rate Mechanisms" and "Settling Times in Feedback Circuits". For advanced practitioners, read about "Mixed Feedback Designs" and "Combining Feedback and Feedforward".