If you go and study the
actual history of fishing territories, it invariably turns out that they all came/come with complex systems for managing yields. There wasn't ever "a big sea full of fish and anyone could just do whatever they want". For example, if you catch fish with impunity because there is nobody at sea to stop you, you still need to sell them which means interacting the people (in some way) close to where you caught them, and markets have traditionally been one of the points of control.
When so-called tragedies of the commons occur, it is invariably because someone has first attacked those systems of control to further their own ends. In the case of fishing, most traditional fishing communities and systems have objected to the arrival of industrial scale fishing, but they have been ignored and sidelined because of the interests of the owners of those new systems. So the problem is not that people/communities cannot manage resources held in common, it is that they cannot effectively resist power, wealth and greed if and when it arrives. But that very inability is also contingent on broader political and economic conditions, and is not inherent to the fact that the resources are held in common.
Climate change may well be the first true example of Hardin's original concept of "tragedy of the commons". It has a number of properties that traditional resource "extraction" behaviors do not share (including the invisibility of the problem until it is too late). But when people talk about "tragedy of the commons", they are typically referring to much smaller scale situations than the one(s) that have led us to where we are with climate change.
There's also a case to be made, given the remarkably early understanding of the consequences of fossil fuel utilization and the documented behavior of the companies involved, that climate change is precisely the type of failure I'm describing rather than the one Hardin did. We have systems of control for the things fossil fuel has negatively impacted, but people who became very, very, very, very rich from their use actively subverted and captured them for their own purposes.
I acknowledge that the shift is subtle: from the problem being "humans cannot manage resources held in common" to "human systems for managing resources held in common are frequently not robust enough to withstand selfishness and greed". Nevertheless, I think it is an important one.