I understand is that even a Carrington event is not a global phenomenon
Technically, a magnetic storm is a worldwide event inasmuch as the entire magnetosphere is involved. However, you're correct that the effects of the storm can be very localized.
In general, the storm does damage by inducing sheets of current in the earth's crust. A regional effect is that the current density tends to increase at higher latitudes due to the higher magnetic activity in the auroral zones. Unfortunately, much of the industrialized world reaches into the high latitudes.
The induced currents are able to enter the power grid at the points where the grid is connected to the earth. In regions where the crust has low resistivity, the currents *may* stay put within the crust and not enter the grid. However, in regions of high crust resistivity, the grid offers an easier path to the currents thanks to the grounding points. So, another regional effect is introduced: a portion of the grid sitting above conductive bedrock may see a negligible amount of invading current while a neighboring portion sitting above resistive bedrock sees a huge amount. The picture below, from a USGS publication, illustrates the process.
This is where the power industry's interest in "risk maps" comes in. Over the past decade or two, the Space Weather and Geomag communities began combining data on regional crustal resistivity with historical and simulated data of magnetic storms to produce national maps showing how much induced current might be expected at different points of the grid for a given level of storm. The power industry then uses the maps to assess the vulnerability levels within the grid and come up with mitigation plans.
If a major collapse of the grid occurred, a limiting factor of the recovery would be simple human short-sightedness. Around 2005 I was told by an industry rep that full recovery might take decades because 1) the existing stock of replacement transformers is a tiny fraction of the many thousands that would be lost to meltdown and 2) worldwide there are only a handful of manufacturers of said transformers. I hope that The Powers That Be have addressed this issue since then.