Why would I use an electric bike? I live in an extremely flat city that lies about 15m above sea level. One has to drive an hour or two to reach even rolling hills.

Several decades ago, I rode quite a bit, and accumulated a decent "sport touring" road bike, a mountain bike, and a track bike. Then I stopped riding for a couple decades.

Now I have returned to riding casually and found BSE, and it's full of questions about electric bikes, which didn't exist when I was riding before.

I'm healthy for my age. When I ride, I want to be burning all the calories I can. My commute is only 3-4 km. Why would I want an e-bike? What advantages do they offer?
I don't (yet) own an E-Bike, but have spoken to my LBS a few times to find out whats happening in the market. My interest is Mountain biking more than road riding, but the observations probably apply more or less to the same extent. 

1) People who are less fit / non-cyclists get into riding who otherwise would not. This does not appear to apply to you. 

2) In many cases price competitive to non-electric bike - I had trouble taking this seriously then had it explained. People go into a bike shop looking for a bike to lighten their wallet. Evey cyclists knows you quickly get into the $/gram game and end up spending hundreds to save a few grams. Many buyers then turn to the E-Bike rack, and work out they could have a 'decent enough' e-bike made with mid range components for around the price of the light weight racer they are looking at. 

3) Further and longer translates to more fun for the same effort. A recurring theme is cyclists on E-Bikes head out and ride for longer - 4 hours instead of 2, 8 hours instead of 6. The main reason is they are still enjoying riding at the end of a long day because they have not worn themselves out. 

4) Diverse groups - many people worry they are the one holding everyone up, and do not wants to be 'that guy'  (or girl). Rather than join a group they don't ride. A recent event some mates did was a 70km, 2 day MTB ride with a diverse group from diehard's to tag along partners who struggle with 20km rides.  The less fit/confident/skilled in the group rode E-Bikes. The end result was the group rode together, stopped and rested together and no one felt pressured or held up. The ride converted some hardcore 'Box before E-Bike' types to 'Not till I am old and slow' 

5) Fitness - evidence is building that people who buy E-Bikes gain more fitness than those buying traditional bikes, because they ride more often and longer. I suspect there is an element of the starting point of many E-Bike riders is very low. 

Everyone is different - me, 20 years ao, would have lef tthe E-Bike on teh rack. Now over 50, if buying a new bike, my ego says its too soon.... Couple of long hard rides I might get it to change its mind.