That only works if you can separate responsibility out to the extent that each person is responsible for a specific area of the code and works only on their designated area.

What happens in practise is that a feature or bugfix might require a large change to one part of the code and a much smaller change in another.

So the developer tasked with the small change will finish before the other. Now you have an idle developer and an overloaded developer holding the process up. If you have a process whereby the idle developer can't share some of the workload of the other you are going to have very inefficient development.

You also run into problems if one developer is on holiday , off sick or leaves the company since nobody else has ever looked at their code.

There's also a risk of bringing politics into re-factoring decisions. "This functionality should be part of your API".