How to get view count and most visited sites at a web application level as a whole in SharePoint on premises.
Other than Popularity Trends is there any other way to achieve this?
You should get to know about Google Analytics, Google Analytics is a web analytics service provided by Google and the most interesting part is, it is a freeware. It can be used to track and report the website traffic.
You may get lots of blogs regarding Google Analytics for SharePoint. Listed few below,
https://www.harepoint.com/Articles/GoogleAnalyticsSharePoint.aspx https://zimmergren.net/integrating-the-google-analytics-api-in-sharepoint-in-order-to-enable-users-to-review-analytics-data-directly/ http://www.letsharepoint.com/how-to-enable-google-analytics-in-sharepoint-2013-office-365/
"Use Google Analytics" is the easy answer to this question. However...over the past few years Google Analytics has morphed into more of an advertising tracking solution than a web analytics solution, which means it isn't a good choice for SharePoint Intranets. Plus, GA's Terms of Service doesn't allow you to store usernames in the reports.
SharePoint sits on top of IIS, and the IIS web logs contain the information you're looking for. Just find a way to process the IIS logs, and you'll be all set.