They didn't go through so much extinction as Pteridophyta, but their speciation rate still much slower than later one. Can we understand that by genomic analysis? Such as unique genome structure influences the evolutionary rate etc.
I think one line questions like this one which are very broad is easy to ask, but to put forward the idea why the question is being asked is also an important point to think and consider.
What what is the rational about genomic analysis, how and what do you want to do that?
Genomic analysis is a very vague expression in the context of this question.
It's a difficult question since there are approximately 1000 species, which is a lot compared with some groups, but not as many compared with others. So it's relative. More importantly, we will never know 'why' (a teleological question) unless we knew the exact processes that resulted in their creation and could ask God. Definitely the trees cannot tell us :)
as a palaeobotanist I would be reword your question as:
Why do gymnosperms have a low diversity now?
They are there since the Carboniferous at least, ca 400 million years ago. Several families have disappeared today: Hirmeriellaceae, Voltziaceae, Palyssiaceae, etc.