E-bikes eliminate two factors that inexperienced bikers struggle with: wind and hills, two things that a couple hundred extra watts really help with even when limited to 20-25mph.
Especially if you are towing a burley or have panniers or aren't in full spandex. The wind resistance really adds up.
Ebikes are such an effective and useful form of urban transportation that very efficiently leverages what battery supply we have for cheap and FUN travel. To the point that the government should make this the "summer of the ebike" and offer a $500 rebate on e-bikes this summer.
When I lived in a downtown, I could not wait for bikeable weather to come (midwestern winters). A city shrinks by a factor of ten over walking, and when you consider you often can park right by your destination for free, while cars almost always have a 10-15 minute penalty for finding parking and walking from the parking spot.
The convenience range of an e-bike that can do 250-300 watts over a regular bike is probably 20-30 miles further, especially when often bike routes can be more direct.
And an ebike gives the horsepower to cart around rain gear.
For things like watching marathons, parades, and festivals (as long as you aren't THAT GUY trying to walk his bike through shoulder to shoulder crowds), they are unmatched. You get so much more of the experience.
Of course so much of this is because people don't bike, maybe things would change if a lot more people did.
If you are ever doing the tourist thing in Washington DC, their city is perfect for their bike share service. It was AWESOME. Being able to go monument to monument, smithsonian to smithsonian, to the zoo, to the hotel, to restaurants, was amazing on a bike with no hassles with car parking, the roundabouts in cars, or dealing with the metro schedules and line transfers. Bonus: you can go to Georgetown easily which doesn't have a metro.
Manhattan/NYC SHOULD be like this, but it wasn't in the same league as DC last I did it. Brooklyn was still not well served.
Manhattan/NYC would be much better with an ebike. It would shrink Manhattan neighborhoods by a huge amount.