Why is it so important that an amplifier is unconditionally stable?
We like to pretend that circuits such as amplifiers are essentially linear around some specific operating point, because that vastly simplifies their analysis. However, like many things in electronics, that is only an approximation.

That approximation fails to a certain extent with large input signals, and to a greater extent during transient events such as power-up and power-down, leading to undesired behavior in real-world circuits. Therefore, we use conservative margins in our designs, including such rules-of-thumb as requiring unconditional stability.

As always, the "principle of least surprise" applies for others who may need to deal with the circuit.