Long distance trade declined toward the end of the Late Bronze Age — and in the Early/Middle Iron Age was increasingly carried out by private merchants rather than state-sponsored expeditions — but continued nonetheless. Imported materials like lapis and tin were still available and used in the Early Iron Age.

To quote Sarah Murray’s The Collapse of the Mycenaean Economy (2017),

>Snodgrass originally argued that the use of bronze in Greece decreased after the LBA because the supply of tin, which must have been brought to Greece from far away to the East or North, was cut off at the end of the Bronze Age, forcing Greeks to find a new metal from which to make their tools and weapons. According to this bronze shortage theory, trade routes bringing copper and tin to Greece broke down just after some areas of Greece had learned the art of ironworking from Cyprus. When they could no longer obtain copper and tin, Greeks turned their metallurgical attention to forging iron (in places like Euboea where they had learned how to do it) or to the recycling of old Mycenaean bronzes (in places like West Greece where they had not). Bronze became more abundant again when trade with the east was reestablished around 900.

>This theory has been controversial. Morris questioned the bronze shortage hypothesis on the grounds that it draws too simple a connection between deliberately deposited metal artifacts and originally circulating quantities of metal. He argued that the prominence of iron in burial assemblages during the EIA reflects new social strategies that were put into place by an emergent elite that used a different metal to set itself apart within society. In this view, the use of iron for tools and jewelry was not the outcome of need generated by the lack of a preferable metal, bronze. Rather, changes in the socially determined meaning of metals led to different types of deliberate deposition, which is what we see in the archaeological record. We might also imagine that as iron became more common in the PG period, demand for bronze would have declined, because metal made from a local ore had replaced many uses of the old exogenous resource. In any case, the notion that tin was in short supply in the EIA has found little support from analyses of bronze objects, which have normal to high tin contents. Snodgrass has now stepped back from his original position, and most scholars have followed suit, questioning just how much access to tin waned…

There was a pollen grain analysis study published a few years back that indicated a broad regional climatic shift, drought, and subsequent widespread famine resulted in mass migration. There are also cuneiform tablet correspondences between Near Eastern empires and Egypt in that time period attesting grain shortages and general civil unrest. So it's less likely that it was a disruption in tin trade directly that ended the LBA and more a breakdown and collapse of trade networks when hungry, angry people abandoned cities and went looking for "greener pastures".

This is a very general summary and it's actual way more complex than just sea people are climate refuges but I'd happy to talk more in-depth.

I have similar suspicions. I've thought about how a small number of elites with bronze weapons and armour could control the masses. I can also imagine them suppressing iron technology. However, once one empire lost control, iron weapons and tools dispersed quickly, insurrections happened, and the whole house of bronze collapsed.

I've read (in the Penguin atlas of ancient history, the Sumerians lost access to tin at one point and fell temporarily back into the Chalcolithic.)

It was the tidal wave that wiped out Crete. The Minoans were the copper plug from their incredibly pure mines in Michigan. No copper no need for tin.