If you just have the access permission and the main owner is incapacitated or dead, your access is not valid anymore and it's a huge hassle to get access to the funds.

You want the co-owned style where both have equal rights to the funds on the account. The easiest way to check it is just to contact your bank and make sure it's set up that way the exact terminology seems to vary a bit between banks.

It's much rarer now because checks are basically gone, but you used to be able to get accounts that would require both signatures on the check, not just one.