The shortest answer is no you don't need to purchase car hire excess insurance when renting a car. Your vehicle rental will include a basic insurance product under the name of something like collision damage waiver (CDW) or Loss Damage Waiver (LDW).
This cover can differ between company to company but will ultimately offer insurance cover in the unfortunate event of a collision or damage to the rental vehicle, sometimes this includes theft as well. You should always read the small print when renting a vehicle and this will detail what is and isn’t covered by the included basic insurance as in most cases the cover will be fairly limited.
The CDW / LDW cover offered as standard with a vehicle rental come with an excess and sometimes this can be fairly high (as much as £2,000) and its this fee that a car hire excess insurance policy protects against.
When purchasing a rental vehicle online or picking up said car, the provider will offer you additional insurance options to cover the shortfalls in their basic insurance product. The independent car hire excess insurance does exactly the same except packages several extras into the one product usually at a cheaper price.