Tank Destroyers should be faster than tanks. In general, they were made using the chassis of light tanks, but with much lighter armor. The entire point is that they're cheaper and faster. Why else would these units exist?
I agree with you, but do some searching here and you will see there have been a few discussions about them. Apparently the Axis version of a tank destroyer was slow and heavy, while the allies were fast and light, So it appears we have the average of those represented in a unit that is slow and light.
Now if @freezy would like to add a discussion of tank destroyer speed to the next round of updates, I will be the first in line to chime in. 
The German Marder III and Hetzer tank destroyers (the two primary German Tank Destroyers of WWII) were faster than the Panzer IV, and all prior German tanks.
Oh I am not the historian, don't take my word for it. There are plenty of participants here who know a lot more than I do about such things. 
You might look at this thread from two weeks ago about the same topic.
You also have to account for the Russians. They also favored a mixed tank destroyer. Some where made to be fast and others were made to take a beating. The tank destroyer was short lived however. Anti-tank guns were cheaper and easier to get. Not only that but more effective. You could put them in towns and they did very well in close range combat. The tank destroyer was not good in towns, was harder to make, and cost much more. So for the anti-tank role, all in all the anti-tank gun was better.
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