It really depends on scale. If you run a small site, one that gets less than 10 million hits a month or so, you're fine on a run-of-the-mill CMS like Wordpress. Though I should mention many frameworks will fall over at much less load due to poor design decisions.
It gets interesting when your concurrency goes higher. Things like ORM baked into many frameworks break down, and if your site is interactive, it's a lot harder to add effective caching.
Over the last six years I designed a Linux-Nginx-MySQL-PHP stack that currently does over 2 billion requests per month. Over 98% of the requests are served entirely from cache, and every request gets a live view (no reverse caching proxy or the like). This is possible because I designed and basically scratch-built a framework that does caching intelligently, in a way that's just not possible with any ORM-based framework I've seen. The front-end is mostly JS, which I did not build, and it does use frameworks like jQuery, angular, less, grunt, etc.
We're starting to see mild growing pains (but we could still handle ten times our current traffic) and are migrating to a Cassandra/Kafka/Storm/Java stack to take things multiple orders of magnitude higher and to make everything real-time. There are simply not any frameworks available, but there are many projects like Cassandra, Kafka, and Storm that do a lot of the hard work and that can be glued together with you own libraries.
It doesn't take a huge team to do it, either, if you're smart. We're a dozen people on the tech side, including design, front, back, ops, QA, and management.