Do you mean "There is no need to use the value of time period that is LESS than Ta" or "NOT LESS than Ta"?
As you quoted FEMA 451, it says
Ta is lower-bound limit (more conservative for base-shear as T-computed would be higher)
CuTa is the upper-bound limit (can be ignored for drift calculations)
But,
There is no guidance on if T-computed is less than Ta, not even in ETABS manuals. All the documents highlight the upper limit but not the lower one.
For example, consider a bearing wall building, (density of walls/floor is large), T-computed is ~ 0.10s, however Ta=0.5s; huge difference.
ETABS only checks the upper limit (lets say 1.0s) and not the lower one and selects 0.10 automatically and calculates base shear for this T.
However, if I am getting you right or as per; 2009 NEHRP Recommended Seismic Provisions; Chapter 4, page-41, it says;
if T-computed is less than Ta, then use Ta.
https://www.fema.gov/media-library-data/1393888487069-c071850c3050c34da135376baa478a1b/P-752_Unit4.pdf
Please shed some light on this issue.