GPS receivers can get very accurate velocity vector information. It is part of the receiver architecture, and does not require a separate processing of prior positions.
So the velocity information is "free" and actually is much more accurate than the position information.
From a global architecture standpoint, it is far preferable to provide the velocity vector than it is to defer the calculation to a ground station, and because of the accuracy, it is desirable to use the velocity vector from the receiver rather than to rely of historical points to calculate that velcity vector value.
Those are factors in the architecture of ADS-B and the data fields.
Addendum #1: The OP asks, "Since the velocity of an aircraft can be computed from two successive position broadcasts, why is the velocity transmitted directly?" There are two parts of the answer. The first is that the velocity information is available from the GPS receiver and is magnitudes more accurate than the position estimation, and happens at a much higher rate than the position estimations needed for a velocity estimation. The OP surmises that successive position estimates can be used for a velocity estimation, but a velocity estimate determined that way will have substantial error, and latency. The second is that the standard says that velocity information will be transmitted. Of course it was designed that way because the continuous, low latency and high accuracy velocity information was available from the GPS (utilizing the Doppler of each SA L1 carrier against the local clock or other method).