In large organizations, it is quite common for employees to have a narrow and well defined set of responsibilities, as the organization needs to keep a vast amount of workflows well organized and avoid rework, mistakes and the subsequent lack of productivity and increased cost. So a model like the one you describe in a large company seems odd, at least in a great number of cases.
Conversely, small organizations need to be quite flexible to survive. Communication paths are well defined because teams are reduced, so changing hats is sometimes unavoidable and does not cause major problems, as everybody has a good clear visibility of the rest of the team and their work.
Also, small organizations are particularly sensible to absences (annual leave, sickness, another employment, or unforeseen activities,...) or changes in the organigram, and the entire organization may be impacted.
That's the most probable underlying reason why your boss wants to have several people with the ability to change hats if and when required, because he wants to ensure that the organization stands a sudden layout change.
So although the model in your company is not common, it is also pretty understandable. In the meantime, you should be quite happy that this is happening and take advantage of it. You will:
- Learn different roles.
- show in your profile that you are flexible.
- Contribute to understand the processes from different perspectives (developer, lead,...) and understand what are the challenges.
As a side note, you may suggest to use your shifts when you are not the lead to act as an auditor of your current leader. He manages, but you may also do a sanity check in your/his work. This happens in the aeronautical industry, where the Captain often hands over the control of the airplane to the First Officer. Captain is the ultimate authority but FO is in charge of controls, and acts as a second pair of eyes. This is the ultimate reason why there are two pilots onboard. Think about your role in the same way.