Your making the 100% reserve backed case here. Time deposits are inherently risky in an investment sense - you have to be sure that the bank is making prudent loans in order to get your money back at the date of maturity, and you might not be able to get it back before maturity, even with a steep fee.
Alongside of that would be 100% reserve backed demand deposits, which the bank would keep in specie at all times (meaning they would have on hand 100% in gold or whatever commodity of all demand deposits, not that they would hold specific monies for you). These deposits would be treated as a bailmant and so could not be used by the bank for operating expenses. They could also be insured against theft or destruction or embezzlement, as these are both insurable events (unlike fractional reserve banking, which can only sustainably be insured by gov’t as there is no way of predicting the severity or timing of bank runs, they are scalable random events instead of gaussian ones).
There should be risk in making a loan to a bank (through time deposits - after all you are getting a return on your investment), but most risk from demand deposits (barring bankruptcy of the insurance company) could be eliminated.