> I know the classic cryptocurrency trope is that Bitcoiners will move money to a paper wallet and then store the passphrase securely somewhere, but in reality that's about as attractive as cashing it out as 46 x (hypothetical) $1 million dollar bills and storing it in a safe.

That's very hypothetical, though. There are a few key differences:

1. Moving money to a paper wallet is not difficult in practice. Ideally, yes, you would generate the private key in an air-gapped computer running a secure operating system and print out the private key and the Bitcoin address, then incinerate the computer, storing away a second identical computer that doesn't have the wallet on it yet, and that would have a similar level of difficulty to buying and installing a safe. In practice, you can probably get better security than a physical safe just by generating a new wallet in Electrum, writing down the seed phrase, and deleting the wallet from Electrum. When you need to spend some of the coin you can reanimate the wallet, sign a transaction, and delete it from Electrum again. If your cellphone is backdoored then the thieves can loot your wallet at reanimation time, but that's probably harder than drilling a safe, most of the time.

2. As you point out, million-dollar bills are hypothetical. The largest US dollar denomination ever printed was US$10k, and the largest in circulation since 01969 is US$100. So, in practice, you're talking about a safe containing 460,000 US$100 bills, which will be very difficult to either acquire or dispose of without getting robbed.

3. The dollar inflates, by design, so it's a terrible investment. It's lost 96% of its value since the end of the gold standard in 01971, and an additional 6.2% over the last year. That's the reason why a safe full of dollar bills is a total failure for wealth preservation. Bitcoin suffers from a lot of volatility but it's structurally designed to not suffer from secular inflation, and in fact one of the principal criticisms of Bitcoin is that it's inherently deflationary. It seems to have returned an average of about 150% per year over the last 10 years: https://bitcoincharts.com/charts/bitstampUSD#tgSzm1g10zm2g25..., and while that trend surely must be nearly over (it can't continue for more than another 5 years and might already be over), it also clearly hasn't been suffering from inflation. In this sense, the most important difference, the dollar and Bitcoin are opposites.

Yes, it's true that there are people who like to gamble by day-trading cryptocurrencies, but most people who do that end up losing all their money. Investing wealth doesn't require your assets to be "accessible and tradeable on short notice"; it requires rebalancing asset classes every three months. Berkshire Hathaway makes a few dozen transactions per year. You don't need to make more transactions than Berkshire Hathaway.

You say, "there are many, many people out there storing vast amounts of wealth accessible by 2FA with their phone and it's rarely ever a problem," and in a sense that's true; it's relatively unusual to have a meltdown like the Argentine collapse of 02001 (where all bank depositors lost all the dollars they had in the banks), Mt. Gox in 02014 (where all Bitcoin depositors lost all their Bitcoin, about 850,000 BTC or US$450M), Bitfinex in 02015 (where their depositors lost about 1500 BTC), the Greek banking system in 02015 (where Greeks were prohibited from carrying more than 3000 euros out of the country and could only withdraw a limited amount of cash from their bank accounts for three years), and Bitfinex in 02016 (where their depositors lost 119,756 BTC).

But it would be a terrible mistake to conclude that, just because an event like this happens only about once every four years, it is unlikely to happen to you. It's true that it's "rarely ever a problem", but when it is a problem, it's a problem for millions of people, sometimes hundreds of millions. Hosted wallets do not and cannot offer "reasonable security".

Today I see a lot of people who are "trading Bitcoin" but actually holding Tether in Binance accounts (which has replaced LocalBitcoins as the retail hosted wallet of choice here in Argentina).

Tether has historically been backed by fraud, and it's operated by Bitfinex, which (as noted above) has a history of its customers' money mysteriously disappearing, and which is locked out of the world banking system.

Binance is banned in the US and UK, is being criminally investigated by both governments, and has had to move its headquarters from China, to Japan, to Malta, which also says they're investigating it. It's also being prosecuted in Thailand.

Without casting any aspersions on the integrity of Binance's people, it's clear they're at significant risk of having their assets confiscated, at which point all of their depositors would lose their deposits. And Tether is at significant risk of collapsing, either due to fraud or to mismanagement. So these people are dancing on a tightrope, and most of them don't even know it.

So, run a wallet on your own hardware. At least a thin wallet like Electrum. Or get a Trezor.