Electrical – STM32L4 Clocks Configuration

Clocks are used in computers for the simple reason that most if not all of the circuity is synchronous sequential logic.

In a synchronous circuit, an electronic oscillator called a clock generates a sequence of repetitive pulses called the clock signal which is distributed to all the memory elements in the circuit.

Now, that may not seem satisfying and granted, you would reasonably ask "why are synchronous circuits used in computers?" but that's an easy question to answer too:

The main advantage of synchronous logic is its simplicity. The logic gates which perform the operations on the data require a finite amount of time to respond to changes to their inputs. This is called propagation delay. The interval between clock pulses must be long enough so that all the logic gates have time to respond to the changes and their outputs "settle" to stable logic values, before the next clock pulse occurs. As long as this condition is met (ignoring certain other details) the circuit is guaranteed to be stable and reliable. This determines the maximum operating speed of a synchronous circuit.

An active area of research is asynchronous computing where most if not all of the circuitry is asynchronous sequential logic.

NFC has an inherent protection against man-in-the-middle attacks

This is not true. There is absolutely nothing in NFC that would protect you from man in the middle attacks in any way.

Regarding your main question: doing ECDH on any modern microcontroller is much faster than your NFC link can transfer the data, so don't worry about performance here.