Should I upgrade my wiring when installing a new speaker or amplifier? 

It depends on the scope of the upgrade.

Speaker upgrades only: If your factory wiring is in good condition (no corrosion, damage or poor connections), it is generally safe to reuse it when installing aftermarket speakers.
Amplifier upgrades: When adding an amplifier, upgrading wiring is strongly recommended. High-quality power, earth, speaker cables and RCA interconnects ensure; Stable power delivery, Reduced noise and interference and improved reliability and performance. Focal offers a complete range of wiring solutions, from PK8 and PK21 performance kits to our Elite Series speaker cables and RCA interconnects, designed for uncompromising signal integrity.

https://focalaustralia.com.au/product-category/accessories-cables