Normally the transformer should be protected from a major damage - there are fuses to blow before the transformer does. However these are not always sufficient, but likely most of the time. So it would not be all transformers down, but only a few percent of the ones that sit at long lines, and quite a lot of blown fuses.
I guess all mains-transformers are protected against lines failing short or open, the longer the wire, the higher the probability of a failure - there is no solar storm required to cause a huge spike in current. Lines falling on each other is an everyday thing on a larger scale.
Common mode rejection might be relevant in such a situation, but its not only the wires that are hit, it´s also the ground, so relative where is that big increase coming from, in a ground referenced circuit?
And i kind of doubt that it would be much worse than in a typical thunderstorm, which is basically the same (atmospheric charge/discharge gets added to the system) and is huge enough to cover a segment of a grid. Of course it is one grid, but it is a segmented grid and the usual electrical installation has a protection that matches that segments size. I don´t see where a solar storm overload should differ from any other overload. If someone doesn´t protect properly, it would have failed anyway, as this is not a "80% of the maximum performance yields 80% results" type of calculation, it either fails catastrophically or it doesn´t.
Also there is a certain mass of atmosphere and humidity in between space and ground always covering a certain percentage of the exposed area, possibly dissipating large chunks of said energy.
50% of all orbital satellites (the ones between sun and earth, not behind earth) are probably more affected by that problem than ground installations, even if it´s just a decrease in lifetime.
Still the grid would be down and it could take some time to restore the fuses and to bring up something like 98% of the grid that is still intact (some of the blown transformers are spare anyway).
Any power plant needs to be connected and then serviced once in a while, therefore bootstrapping should be a regular procedure anyway.