Absolutely. The other day, I took my slow Wordpress server hosted at Vultr on bare metal (£200/pm) and put it on a server at £500 per month and even after doing all the performance tuning I could with MySQL and PHP I couldn’t notice a difference in speed when I was on the back-end where Cloudflare wasn’t caching it.
I then tested on a lower performance server which costs £80 per month at Vultr and again couldn’t detect any difference when in the back-end.
No matter what performance tuning I done, I couldn’t make it work faster for us. But at least I am on an £80 server instead of a £500 server I guess.