Such information is stored in a secure place in the legal system and is not accessed by anyone until the start of the legal process.
You're certain? There's no way that someone might glance at it in a filling cabinet somewhere? Or that it might get scanned and uploaded to server, and someone might take a look at it? Or when you are updating your Will that an intern somewhere might be handed the old copy to shred? I would never hand over your seed phrase or keys in plain text to a third party, regardless of how reputable they are or what processes you think are in place. Things go wrong and things slip through the cracks all the time.
It is easy to criticize both solutions but what then do you suggest as an alternative?
What I have outlined above - encrypted seed phrase with heirs, decryption key with lawyers or other trusted third party. Alternatively, a time locked transaction. I set up a transaction moving all the coins in my cold storage to my heir's address, but timelock it so it cannot be broadcast before block 741,000 - roughly one year from now. I hand this transaction over to my heir. Once we hit block 741,000, they can broadcast it and claim all my coins. If I am still alive, then at some point prior to block 741,000 I move all the coins in my cold storage to a new address, thereby invalidating the timelocked transaction they are holding, and provide them with a new timelocked transaction, this one unable to be spent prior to block 795,000, roughly another year on. Timelock can also be performed with Unix time if you want to be exact and don't want to depend on the variability of the average block time.