This article describes some tradeoffs involved with methods to increase an amplifier's linearity. One of the ways to increase a circuit's linearity is by applying negative feedback, which converts an amplifier's uncontrolled open loop gain \$a\$ to approximately\$1/\beta\$, a value which can often be much better controlled independent of the input and so the amplifier is linearized. The article describes a tradeoff with high-frequency operation:
To make the closed-loop system stable, we have to apply frequency compensation techniques to sufficiently reduce the loop gain to below 1 when the loop phase shift is 180°. This is conceptually equivalent to placing a low-pass filter in the loop. Low-pass filters suppress high-frequency signals, therefore, we expect the operation frequency of the closed-loop system to be much more limited than that of the original uncompensated amplifier. To summarize, applying negative feedback increases linearity at the cost of reducing the frequency of operation.
I understand that when considering the open-loop system on its own, in order for it be stable when put in the feedback loop, generally its bandwidth will need to be significantly reduced. However, another main benefit of closed-loop operation is bandwidth enhancement. For example, with a simplified first-order system, the bandwidth of the closed-loop system is \$1+T\$ times better than the open-loop system, where \$T\$ is the loop gain.
In light of that, is the article saying that in practice, the factor by which the open-loop system's bandwidth will have to be reduced for stability reasons is much larger than \$1+T\$, therefore overall reducing the overall bandwidth?
