EGR cooler nightmare event -- always check a used one for leaks before you install...

It is possible the cooler was defective. Maybe not a good weld somewhere.
It's very doubtful the piano wire poked a hole in the cooler lines. Unless you used a drill
and left it at the exact same place for very long time is it just wore through.

Because oil gets by the weaker oil rings on the piston, and gets burned and eventually clogs the
cooler because the passages are small. They are larger in the Gen 4 and above models. And
the rings are better so you don't have the oil blow by.

When the cooler clogs, the exhaust has nowhere to go and builds up so it will reach the cylinders and
creates more back pressure and can cause more pressure in the cylinders. And when the egr vavle opens
even more exhaust can possibly get sucked in through the intake manifold. But those small ports also
clog. Like putting a potato in an exhaust pipe. The engine will eventually shut down.

In theory, in the late 2014 and 2015 engine Toyota fixed the issue with the rings. But they still have some
head gasket failures. I personally think the longer change times, and the type of coolant used supposedly
to last longer, eats away as the head gasket material. But it's kinda funny that in 90+ of the cases
it happens between the #1 & #2 cylinders.

It's likely the head gasket was failing when you cleaned the egr system. It was just a coincidence,
unfortunately, for you.

Perhaps it was a good thing. Because had you not done the cleaning, you could have had more damage
to the engine as more coolant could have gotten into the cylinder and could have bent 1 or more rods
or through it through the block.