There is, unfortunately, no “pretty” way to do this (i.e. without using string replacing or rewriting a big chunck of functionality). So, resorting to preg_replace
…
We’ll need to filter the links, and it’s good to see that you’ve already found the proper filters! Looping through the views and using a regular expression, we can remove the element containing the post count. Implementing this for posts, you’ll need something like this:
add_filter( 'views_edit-post', 'wpse149143_edit_posts_views' );
function wpse149143_edit_posts_views( $views ) {
foreach ( $views as $index => $view ) {
$views[ $index ] = preg_replace( '/ <span class="count">\([0-9]+\)<\/span>/', '', $view );
}
return $views;
}