P3 Profiler and Yoast SEO plugin

Now I do have quite an aggressive caching turned on with WP Super
Cache. Does it still matter if I force-rewrite the titles then? Or in
my case it doesn’t change a thing since pages are pre-generated and
served as static content?

Yes it does matter because you are not serving cached content 100% of the time and you also have to think about the time and resources it takes to rebuild the cache.

You eliminate the need to force title rewrites by fixing your theme and replacing whatever is currently being used in the title tags with:

<title><?php wp_title() ?></title>

I’m leaving wp_title() blank without any arguments because the plugin is going to filter that content anyway.