[vvillena]

That's correct, but there are some extra considerations. Usually, a Bitcoin wallet will generate multiple addresses with different private keys, using the initial key as a seed alongside some extra parameters. The only real-world ramifications of this are that there could be compatibility issues between different wallet software, meaning some extra configuration is needed before being able to regenerate the wallet.

[corobo]

... and people were trying to convince everyone this is the new currency at one point

[vvillena]

What I described is the complete procedure for regenerating a wallet set, from zero. If you want a real-world equivalent, it's like teleporting all the gold you own to your hand at any time. You might think the procedure is a hassle, but the reality is that you will have a well-secured computer as your primary storage. Being able to recreate a safe store out of thin air is just icing on the cake.