But our link count has been this high for a long time.
Are you happy with your site's current SEO performance? If so, there is no need to change. If you wish to improve your site's SEO, I would suggest your link structure is a major issue.
So you are telling me, that if i decrease the link count my page will have a higher authority?
No. Your authority remains the same whether you have 1 link or 1000. The difference is how that authority is distributed throughout your site.
The concept of optimization is about prioritizing. You want the most link juice to go to the most important pages such as your money page, official interviews, and the most popular articles.
The trimming of links is most important on the homepage or should this be done on each and every page?
It should be done of every page. It is more important on the home page, but it affects every page.