Can US citizens use the electronic passport gates at Heathrow airport without having to enroll beforehand in any special programs?
You will be able to from Summer 2019 says this article on the UK government's website, I'm pretty sure it used to say April 2019 (not 100%) though.
But at the moment you cannot use these gates, you have to see an immigration officer in the All other passports queue, unless you are a registered traveller.
From summer 2019, eligible travellers from Australia, Canada, Japan, New Zealand and the United States will be able to use the ePassport gates at 14 ports, both in the UK and at Eurostar terminals at Brussels and Paris.
I will update the answer when this comes into force.
Update May 2019
As of 20th May 2019, citizens of Australia, Canada, Japan, New Zealand, Singapore, South Korea and the United States can now use ePassport gates, including at Heathrow.
From today (Monday 20 May), visitors from Australia, Canada, Japan, New Zealand, Singapore, South Korea and the United States will be able to use ePassport gates at ports across the UK and juxtaposed controls in a move designed to speed up border controls for low-risk countries.