Self-custody is the original argument for crypto: an asset nobody can confiscate, freeze or inflate away at will. The phrase "not your keys, not your coins" summarises it, and the long history of exchange failures supports it.
It is not free. You assume the jobs a bank does invisibly: backups, physical security, inheritance planning, and resisting social engineering. Losses from user error are permanent and, judging by long-dormant supply, substantial.
A sensible split for a trader: working capital on venues you have diligenced, long-term holdings on a hardware-wallet with a tested backup, and a written plan for what happens to the keys if you are unavailable.
Related: non-custodial-wallet, hardware-wallet, seed-phrase, custodial-wallet