Site speed is important. It is one of our key mantras.. Speed, security, stability.
The faster your site loads the more money you make. It is one of the reasons we as a company exist. After years of development we can tweak sites / servers to run faster than our competitors.
To this end we are encouraging everyone, where possible, to move over to php7. Since its release in December 2015 php 7.0 has morphed into 7.0.10 released in August. This is now the official supported version of php and all sites should be moving to this. Php 5.4 and 5.5 are dead with no further security releases and support for 5.6 is due to end at the end of the year (don't worry security fixes will follow to end of 2018 (source)
Php7 is a big deal. In light of strong competition from the HHVM project php needed to do something radical to ensure it continued to be the default engine powering the majority of the internet's sites. Switching to HHVM has giving dramatic boosts to many stores and php 5.6 was looking to be a poor option. Then along came php7. Which allowed dramatic increase in proccessing of php scripts. This brings the Zend php engine to similar speeds of HHVM in many cases doubling the speed of sites over php 5.x.
Thanks to the new Zend Engine 3.0, your apps see up to 2x faster performance and 50% better memory consumption than PHP 5.6, allowing you to serve more concurrent users without adding any hardware. Designed and refactored for today’s workloads, PHP 7 is the ultimate choice for web developers today.
Magento 2 supports php 7 out of the box and all new Magento 2 sites run this version. While Magento 1.9x is not immediately compatable with php7 it is generally possible with a few tweaks to run your Magento 1.9x store on php 7.
In most cases installing this module is enough : https://github.com/Inchoo/Inchoo_PHP7
Once installed php can then be switch from 5,x to 7 (jsut raise a ticket) and you can immediately benefit from the increase in speed. Even sites running a full page cache can benefit from the increased (and critical for conversion) add-to-cart speeds.
It is possible that one of your existing extensions is not compatable with php7. The only real way to find out is to install the above extension and give the site a full test. If there are problems with an extension you can then decide if the increase in site speed is more important then the extension.