While I understand your point, the reality is that there are often investors from the first fund that get transitioned into the second fund. So for them, this 'composite' performance is entirely relevant. But you are correct in that it means you have to be careful when looking at historical returns.
From a technical perspective, a fund is a legal entity. Changing from one investment manager to another doesn't affect the legal entity (i.e. the Trust involved). But it does make easily understandable difficult!
