Why do we need to know the Population Variance for the finding CI in T distribution? We can find it with the formula and we can proceed through Z value insted T Value. sigma^2 = (X- Mu)^2/N we can find the population variance with above formula.
Whenever you are dealing with a small sample, you cannot find the population parameters. Therefore, you will not be able to use the Z-statistic.
You are suggesting to apply the population formula, however, it must be applied on population data and not on the sample data that we’ve got.