Absolutely they can be buried. They must be insulated, but that's not particularly expensive. There are thermal limits, as you mentioned, but that simply requires appropriate engineering.
It costs $1 million per mile (roughly) to bury transmission lines. PG&E has about 18,000 miles of transmission lines. That's about $18 billion to bury the lines. Sounds like a lot, but...
...the estimate price of these multi-day blackouts is on the order of $1 billion per blackout. Given multiple blackouts per year, and we're talking just a few years to pay back the price of burying the transmission lines. https://www.sfchronicle.com/business/article/A-cool-billion-...