The short answer is “Yes”.
CDN servers don't just improve performance by accelerating content by selecting the best internet paths, or caching it locally, they do many other things as well.
Without a CDN
How will you handle traffic spikes on days like Black Friday/Thanks Giving Day/Cyber Monday?
What will you do when your Data Center loses connectivity with Internet [in case of natural disasters]?
A CDN can also help you switch over to site without any downtime.
In case of cyber attacks, how will you prevent them?
Why do you want to spend your time and energy on things you do not suppose to be doing?
In today’s world, where anyone can make a botnet and start DDOSing you, how will you tackle them?
Is you server capable of scaling to any number of concurrent TCP connections?
Why don't you just funnel them through CDN servers?
Today, it's HTTP2, tomorrow it might be IPV6, day after tomorrow something else. It's a never ending story. Let experts do their job and you focus on your core business.
Hope this helps in understanding why and how CDN helps in delivering your content over internet.