Would it be inappropriate to directly ask journalists to link any mention of your site in their articles?
There are occasions where I've spoken to writers and provided feedback as a source, and the article doesn't link the mention of the business to the site.
An example: This article on Inc.com that mentioned Bright Journey.
Should sources directly ask for a link when they respond to media queries?
Some publications have a policy that they don't link to companies they mention. It's easy to tell: look at other articles they have written. Do they link to the startups they mention? If so, kindly email the writer and ask them to change your mention into a link. However, be aware that most of the traffic will probably be gone by the time they add the link, if they do. Bu again, asking is free.