If one has something going on such that state-level actors might want nefarious / adversarial access, well, one should be taking MUCH MORE SERIOUS STEPS about personal digital security.
Your "regular everyday normal mfer" (as the song apparently incessantly looped on Instagram goes) has no such enemies. My personal digital opsec is designed to keep me and mine safe from likely threats, and the threats I face are pretty banal -- brute force attacks, mostly. I am 100% unconcerned about governmental intrusion into my safe to gain access to, e.g., my online banking passwords.
It's not paranoia. That would imply they aren't out to get you. They are. Leave the government out of it for a second. If someone's phone is stolen it's very likely their entire identity, a majority of their secrets, documents like medical ID cards, credit cards, etc have been compromised. This is akin to "getting a warrant to a safe" (which in reality is just court-ordered theft) and it will completely destroy a person. In the context of the discussion if you were able to break into a dead person's phone you could very likely build a complete picture of their life. Perhaps one they weren't interested in you knowing about.
I'd prefer to avoid those situations. First, by not making myself a target, and second by protecting any and all data I have the best I can. I rarely think about it but I know if my phone is stolen, my computers are taken, or I get caught up in a fishing expedition the threat surface is extremely limited (provided the information isn't beaten out of me).
It’s simultaneously true that for your model they’re being naive and for theirs you’re being paranoid. That’s fine.
It was indeed from Jon Lajoie, but not the song you link. It looks like he did a followup track called "Everyday Normal Guy 2" which includes exactly the loop you hear (with "motherfucker" and not "guy" in the refrain) everywhere on social media right now.
As the question is about granting access to accounts after death, it seems an odd worry. The government is also likely to get access to your data from your Google, Facebook, etc. If you have a server in the cloud, they can probably go to your hosting provider to get physical access.
So unless you have data in secret offshore servers in countries that won't cooperate with the US government, then a safe is not your weakest link.
Storing secret to password manager that can be easily accessed by government and state actors negates all the trouble that password managers went through ensuring no one besides you can access it. I believe every good password manager encrypts data in a manner so that the provider itself can't decrypt it if government tries to get access to it.
I’m sure others have much better ideas…
In general; you don't. If the gov. wants to make you do something, you're going to have to do it. In many western countries, that's only a vague threat, an many others it's a lot more real.
Theoretically, you could have two components to the password: something long and random that is written down, and something easily remembered and personal. A special moment, a place, an anniversary only the two of you would know, etc.
/s
Government already has access to banking and phone records, most online accounts and data from Apple, MS and Google.