Why is V1 based only on using brakes?
I don't have a proof for the thinking behind the rule making. But my understanding behind it is to prove that the brakes alone can do it in case the reversers are inop. But usually there are exceptions to rules:

dry runways
Dry runway takeoff data does not (with very few exceptions, such as the 737-300/-400/-500 certified to CAA rules) include credit for thrust reverse in the accelerate-stop calculations.
non-dry runways
Historically, Boeing has taken credit for reverse thrust when producing data for non-dry runways. This has been accepted by the FAA. The UKCAA rules, and now the JAA and European certification rules, also allow credit for reverse thrust under these conditions.

For the non-dry rule, Boeing uses half the engines, so for example a 747 would be based on two reversers, and a 737 on one.
Spoilers on the other hand are required so that the landing gears are compressed, if they weren't the tires will slip more. It is also true the heavier the aircraft, the better the brakes work up to their limit.


Quotation and image source: Jet Transport Performance Methods.