Undergrounding can solve this and more.
Consider yourself lucky, in CT for some the outages lasted a few days.
Had Elsa come a few miles closer the story would have been different.
Sure it can solve the lightning problem. I am not against solving problems if an obvious solution exists, but it doesn't here. This is a massive scale infrastructure. Its elementary to look at a problem in singularity and apply it to a system the size of the grid. Simply looking at it an saying "burry it" is a simplistic knee jerk solution. That's not to say it's not a solution but why have this conversation until other options have been debated. You suggested doing this change over 50, 60 or 100 year period. What if there is a nano-tech break through in 50 years with battery tech and it makes the grid less critical? Think about the assumption there. Imagine if the telephone company said the same in 1900. That's static thinking and problems of this scale require critical dynamic thinking. After all the Flint Michigan water utilities are all underground yet have many many issues as do many utilities in city areas. So why don't the cities just re-do those systems? Its not so easy underground. So underground is not a permanent solution without issues.
So without debating a less centralized distributions system, future high efficiency alternatives sources that don't exist yet or other solutions lets focus on what the problem is you would like to fix. Its reliability, but on what scale? Rural? Natural disaster events, all of the above? What does a successful system look like if the current system is below standard? Pointing to localized outages is hardly reflective on the whole system.
Why not simply address the simple issues that create the events you see as problems. So if power lines are blown over increase that standards? Concrete poles seem like a fantastic idea in my opinion. As others have said, putting developments or neighborhoods underground seems reasonable and does seem to be the norm in urban developments today. Trees falling on lines, cut the trees back, raise the lines, or both?
I have zero experience with utilities or the standards imposed on them. Perhaps they have been left to make too many decisions on their own putting the cost/reliability factor on the ragged edge. Perhaps adjusting that a bit so the cost of the service increase a little but the reliability increases by a multiple is worth it. Putting the whole system underground does not make sense. Electricity is our most reliable utility. Its pretty transparent to most of society. That's testimony to its reliability. It can be improved, but I don't feel it needs a complete overhaul. If it does then all options need to be tabled.