I know that I can say "such type of plants" instead of "such a type of plants", but why cannot I say "such person" instead of "such a person"?
Is there any reason for these two different usages of "such"?
I don't believe you can (correctly) say "such type of plants". I believe the difference is singular vs. plural. When you're using the singular (person, plant), include 'a': "Such a person", "Such a type of plants" (In this case 'type of plants' is a singular, the plural would be 'types of plants').
When the subject is plural, you leave out 'a': "Such people", "Such types of plants".