Teamwork is Paramount
When all the members of a technical team are working together, it's so much easier to achieve the goal. This is especially true when it comes to web performance optimization, since so many different technical aspects have to be managed correctly to achieve optimal performance. The strength of a chain is measured by the strengh of its weakest link; a website's performance will also be dictated by the slowest performing component. For example, if database is a bottlneck in your web application, there is no point in putting in a CDN—it's not going to fix the slow database. Instead, you might need a caching layer to take some of the pressure off of the database. Making these kinds of judgement calls takes experience and skill.
Databases are often bottlenecks, especially for write-heavy applications. Experienced DBAs can help tweak the queries or index tables to alleviate some of the pressure. Sometimes adding a key-value store like Redis and storing frequently accessed data in it can reduce the number of times a database is accessed, thus improving application performance.
Systems Administrators can help with using auto-scaling of EC2 instances. In fact, if auto-scaling is used properly, scaling of web servers should become never be a pain point. Use of reverse proxies such as NGINX or Varnish is another excellent way to deal with heavy traffic received by content sites.
When front-end developers work hand-in-hand with DBAs and systems administrators, your site can be be lightning fast.