In 2010, you came across a site that was giving away bitcoins. The site said it was free money so you signed up. You were logging in to figure out how it was money but couldn't. The last time you logged in you had more than 100 bitcoins. Later you forgot about the site until 2017 when a ponzi was advertising Bitcoin. Bitcoin? The name rang a bell and you stated hearing stories. You remembered you must have many bitcoins somewhere but you can't even remember the name of the site. How would you recover your BTC?
Back in 2010 there probably no sites that gave you bitcoins to store in an online account. There were faucets that gave out 5 BTC but those coins were sent to an address that was probably on a full node or SPV client, meaning that you held the keys. Back then the mentality was that
you were responsible for your private keys.
This situation is purely hypothetical.