The problem is that it affects all news feeds, not just Recent Activity. And it messes up the pagination of the feed items. For example, if there is normally 15 items per page, and 6 of the items on a particular page are likes, then that page will only show 9 items.
This is the best you can do with templates. You need an addon to do this properly. If you are a programmer then you can post in the Development Questions forum for help with this. Or post an Add-on Request and some one may be able to write this for you.