All amplifiers have limitations, and two that are relevant are the open loop gain and the gain bandwidth product. A DC gain of 100 isn't too difficult to achieve with one amplifier, but a gain of 10,000 is more challenging. As an example, a standard amplifier may have an open loop gain of 100,000 which means that when amplifying a 1mV signal to an output of 10V, there will be a 0.1mV difference across the inputs (10V output divided by open loop gain of 100,000). The circuit will therefore settle with 0.9mV at the feedback input, and a 9V output. This is quite a large error.

In comparison, using two amplifiers each with a gain of 100 gives smaller errors. The first stage now settles with 99.9mV at the output and 0.999mV at the feedback terminal. The error has been reduced by a factor of 100, which is the improvement in excess gain. Although the second stage will introduce the same error, the overall error has been reduced by a factor of 50.

The issue of gain bandwidth is similar. If the circuit needs a bandwidth of 1 MHz, then the amplifier with a gain of 100 needs a gain-bandwidth product of more than 100MHz. Using two amplifiers, each with a gain of 10 means that they each only need a gain bandwidth of 10MHz.