Treasury Bills (T-bills) does seem like an oddball but it might work for some folks.
I'm going to address it both your questions individually as interest and liquidity.
Looking at the Department of Treasury's site for rates (https://www.treasury.gov/resource-center/data-chart-center/interest-rates/Pages/TextView.aspx?data=billrates, Jan 8, 2019) I see the range is 2.40-2.60% depending on the timeframe (4 weeks - 52 weeks).
This appears mostly comparable to the top savings rates (2.00-2.45%, viewed Jan 8, 2019) found on Bankrate: https://www.bankrate.com/banking/savings/rates/
From an interest perspective, it's essentially the same. What needs to get taken into account are the amounts involved and any special hoops to jump through to avoid fees.
Some of the special savings rates found on Bankrate require a minimum balance. The top rate (2.45%) requires $25,000 balance while the second highest rate (2.39%) requires only $1. Each financial institution (FI) may have their own requirements to avoid any maintenance fees: electronic statements, use debit card X/mo, direct deposit, etc.
For amounts under $250,000, your money is insured by the FDIC (banks) or NCUA (credit unions) if your FI fails. For funds above that, you'll need to either open additional accounts or have them at other FIs to keep your money safe.
T-bills can be purchased in $100 increments, so there is no minimum balance requirement other than the purchase itself. It's also guaranteed by the US Government, so it's considered a risk-free investment (https://www.investopedia.com/ask/answers/013015/how-are-treasury-bills-taxed.asp).
If you have more than $250,000 that you want saved/invested "risk-free", then T-bills could be an option for this, outside the normal channels.
So keeping cash under the mattress has the advantage of being extremely liquid: you can take it out whenever you need it. It has the disadvantages of being insecure and losing value due to inflation (and maybe logistics if you have a very large sum of money).
Savings accounts are also very liquid with one catch: you are limited to six withdrawals per month per Reg D (https://www.nerdwallet.com/blog/banking/how-regulation-d-affects-your-savings-withdrawals/). Transactions in person or ATM don't count in this limit. Your money is kept safe and insured up to the $250,000 limit.
T-bills can be purchased in increments of 4-, 8-, 13-, 26-, and 52-weeks. You won't be able to access your money during that time, but you also won't lose it either unless the US Government defaults. It's the same concept as Certificates of Deposit (CDs).
Hopefully this helps answer why someone might choose one over the other.