I consider myself a pretty strong cyclist, and I was huffing and puffing trying to keep pace with my wife and kids on the ebike.

Having experienced widely varying amounts of power output with the local bikeshare bikes, their varied condition and assisted vs non-, I don't have any illusions here - it's just a different experience to be able to spin it once and feel the bike boost you up to max effort. Even the heavily built bikeshare frames can easily outclass a road bike, if there's no mechanical issue. Although there often is - the chains, gears and tires really take a beating.

I tried my friend's cargo e-bike for 20 minutes in Edinburgh - I didn't even notice that lag. As i turned up the dial for the motor, it just felt like I was turning down the physics! Everything just got magically easier.

The e-bikes here are generally quicker off the mark at lights but that lasts like ten seconds before a decent road bike or legs zips by them because they’re limited to 15kmph

How though? They couldn’t been going that fast.

Most probably it wasn't electric