But as an ESTA authorisation only lasts two years an annual traveller
to the US will only benefit from that once before having to renew
their ESTA. Not quite the same as breezing through UK immigration any
time you visit.
I've not tried entering via the electronic gates in the US as we
typically have our children with us so I have no direct experience of
how easy this is on a second visit within the eligible timeframe.
It's my understanding that as long as you have entered the US one time with an ESTA on a VWP-eligible passport since 2008, you are eligible to use the APC kiosks for every subsequent visit on that passport (and it might even be the case that you can continue to use the APC kiosks when you replace your passport after its expiration, but this seems to vary by airport -- the worst-case scenario is that you have to be processed manually once with your new passport, then you can go back to using the APC kiosks for the life of that new passport).
In other words, you don't have to have entered with the same ESTA -- you just have to have entered with an ESTA.
Incidentally, the United Kingdom also restricts use of its e-passport gates to those who are 18 are older, so American travelers with minor children would also be ineligible to use the e-gates.