Because more words = more official-sounding.
It's a bad phrase that has taken root in irrelevant situations.
Adding "rate" adds nothing in most contexts.
However, the word rate also means "value" or "number".
From Cambridge : rate (MEASUREMENT) noun a measurement of the speed at which something happens or changes, or the number of times it happens or changes, within a particular period
english.stackexchange.com/users/161/Goodbye Stack Exchange
The very first sense for the noun rate in Merriam-Webster is “reckoned value : valuation”.
The word has more meanings than the one used in physics.
One could therefore make the argument that a rate of speed is a speed which is reckoned (i.e. by measuring or reasoned estimation) rather than guessed.
english.stackexchange.com/users/39/nohat
This is classic genteelism .
Speed is the rate of change of position.
Although "Rate of speed" is technically meaningless, it does, however, usually convey the intended meaning (for better or worse).
english.stackexchange.com/users/895/shaunmartin
As a scientist, I would point out that saying "high rate of speed", when one simply means "high speed", is not merely redundant but outright wrong.
Speed is already a rate in itself (the rate at which distance changes).
According to my dictionary*, the relevant definition of rate is the speed with which something moves, happens or changes
* New Oxford American Dicitionary (2nd Edition)
english.stackexchange.com/users/2705/Jimi Oke
In the Ontario Highway Traffic Act, S 128 , the term "Rate of Speed" is used throughout.
I suspect this term did not originate in Ontario, but the usage has become official due to its inclusion in legislation.
english.stackexchange.com/users/2477/Chris Cudmore
Why do reporters (and sometimes police officers) say that somebody was going at a  high rate of speed  when they actually mean  high speed ?  In physics, speed is already the rate of distance over time, otherwise known as velocity. Rate of speed is velocity over time, otherwise known as acceleration. By saying  high rate of speed  they would be implying picking up more speed.  Is there a social reason for using  high rate of speed  rather than  high speed ?
"high rate of speed" or "high speed" to mean going fast
english.stackexchange.com
<synonyms><colloquialisms><hypercorrection>
english.stackexchange.com/questions/2013
english.stackexchange.com/users/457/Ants
It is possible that terms like "high rate of speed" are not just redundant but also incorrect. Such an expression is likely to be used in order to use more words and therefore sound more official. However, correct or not, its meaning is generally understood and indeed it even features in print in the Ontario Highway Traffic Act. The term is technically meaningless and is just used to make the text sound more impressive.
It is possible that terms like "high rate of speed" are not just redundant but also incorrect. Such an expression is likely to be used in order to use more words and therefore sound more official. However, correct or not, its meaning is generally understood and indeed it even features in print in the Ontario Highway Traffic Act. Saying "high rate of speed", when one simply means "high speed", is not merely redundant but outright wrong.  Although "Rate of speed" is technically meaningless, it does usually convey the intended meaning. Yet, interestingly, in the  Ontario Highway Traffic Act, S 128 , the term "Rate of Speed" is used throughout.  
Although "Rate of speed" is technically meaningless, it does, however, usually convey the intended meaning (for better or worse). This is an incorrect phrase, but it is still easily understood and commonly used. One reason may relate to people trying to sound more official in their speech by using more words. In fact, the term may even be used regularly in official contexts in certain regions, such as Canada, for example.
It is just used to impress. It is used to sound genteel. It is technically meaningless. It is used sometimes in official documents.
Saying "high rate of speed", when one simply means "high speed", is not merely redundant but outright wrong.   Although "Rate of speed" is technically meaningless, it does usually convey the intended meaning. In the  Ontario Highway Traffic Act, S 128 , the term "Rate of Speed" is used throughout.  
It might have occurred because people use more words when trying to sound official. This is an incorrect phrase but has become more common. Although it is incorrect, this phrase is still easily understood. This term may even be used in an official context in certain regions, such as Canada.