Let me elaborate what makes WordPress websites blazingly fast. I will share my expertise based on my 7+ years of experience working as WordPress Developer. I will make this blog to the point, without making it extremely long.
WordPress Theme
For sure WordPress theme is the most important part of website speed. Well code themes load faster compared to bloated premium themes. Not to criticize, all the premium themes are slower, but you have to choose well tested and well reviewed themes if you are buying pre-built themes. But nothing beats well optimized customized Wordpress themes.
My suggestion is if your website is business critical then go with a good WordPress developer for custom themes. Else, if your website is simple and only for informational purposes, you can get away with having a website built on premium themes.
WordPress Web Hosting
WordPress web host is another critical part of website speed.
As a Sydney based WordPress developer who has tested several local hosting services, my recommendation will be VentraIP for shared wordpress web hosting. Here is a good article why VentraIP is the best shared WordPress web host. VentraIP is no-brainer if you are thinking of a cheaper but reliable WordPress hosting option.
Likewise if you are looking for high end premier hosting my suggestions would be WP Engine. WP Engine has a solid server and great customer support. And you will get what you pay for. One of my best features with WP Engine is they provide you with 2 servers IP, i.e. they host websites in 2 servers for load balancing, which will be helpful in loading websites when the traffic is higher.
WordPress Caching Plugin
WordPress caching plugin can be a game changer when it comes to loading speed or awesome PageSpeed Insights scores.
I had been a huge admirer of WP Rocket, but recently fell in love with LiteSpeed Plugin. My main reason being the cost of WP Rocket plugin.
My rule when choosing a caching plugin is simple. If you are hosting your website with LiteSpeed enabled shared WordPress web hosting, go with LiteSpeed Caching. Here is the reason why I think LiteSpeed Caching Plugin is the best free alternative to WP Rocket.
I prefer to use WP Rocket when websites are hosted in premium hosting such as WPEngine. WP Rocket performs a lot better in these setups. Here is a bulletproof WP Rocket settings for higher PageSpeed Insight score.
PageSpeed Insights vs Pingdom Tool
There is a bit of confusion when it comes to PageSpeed Insights and real page speed of the website.
PageSpeed Insights is a metric developed by Google and is part of SEO, which mainly focuses on the website built quality around User Experience. It is somehow related to loading speed but does not clearly provide a picture of page speed and performance.
If you need to test your website loading speed my suggestion will be to use tools like Pingdom Tools. Pingdom tools provide an option to test websites from various locations.
Conclusion
Lets be honest, not everyone needs extremely high performing websites. Some businesses can get away with brochure website loading at decent speed.
But if your business is highly dependent on websites for revenue, you have to think about my points above. WordPress is a solid platform and with the right WordPress Specialist, your website will be taken care of but with the wrong choice, you will be losing more than gaining. Cost and quality never come together, choosing the right fit is critical.