There are two major catches: you have to wait at least 1 year before you cash them out, and a person can only buy 10k in I-bonds per year.
After the first year is over, selling I-bonds and getting access to the cash takes a few business days.
I've been tiering my emergency savings based on how many redeemable I-bonds I have. I have enough money in the bank to cover emergencies I might need to pay for very quickly -- things like plumbing problems, car repair, etc. The rest of my emergency fund is going into I-bonds. If I have a longer-term need for savings, like losing my job, I don't need all of my savings right away and I can wait for the amount of time it takes to cash out I-bonds.