Is there a way to sort service requests in the 'Most Popular' view, currently they are shown as the list is an apparent random order?
The sorting is not random and you will only see this behavior with the 'Most Popular' tab. This is the expected behavior.
The 'Most Popular' list add items based on the number of requests submitted. So your most used requests will be first.
Clicking on 'All' or any other category will allow you to see the items in alphabetical order.
The following query will show you that relationship between top items and what you see in that view.
select Name, UsageCount, * from servicereqtemplate order by servicereqtemplate.usagecount desc
In the OOTB data, some of the numbers have been inflated in the table, such as Employee Transfer.