I wrote a longish response to this topic in another thread, but briefly:
I call mine 'the bike that saved my life'. From commuting a hilly 16 miles each way in my 20s/30s, I had had children, been ill and (semi-)recovered, and had lost touch with daily cycling and a lot of fitness. I was overweight, totally out of shape, and at 60+ heading rapidly for the scrapheap. I wanted to get back into cycling, but my new journey to work (13 miles, hilly) would have been impossible on a pedal bike. I wouldn't have made half way. I bought an ebike and did a few trial runs. After a while, I had the confidence to start commuting. It meant 50-55 minutes a day of decent exercise and this, combined with a sensible diet, meant I lost 3 stone last year.
At the same time, I refurbed my 1992 MTB and started riding that on my days off. I now regularly do 15-mile runs on pedal power alone and feel 100% better than I did a couple of years ago. Not much compared to some on here, but a massive change in my lifestyle. If you are ill, or disabled in some way, or even just out of condition, an ebike can mean the difference between cycling and sitting on the couch.
As a point of fact, an ebike is nothing like a moped. On a moped (the older ones) the pedals are there to get you up to a speed where the motor takes over. On an ebike, it's the opposite: the motor helps up to 15.5 mph, and then you are on your own. For probably 80% of my ebike riding, I am just pedalling a very heavy pushbike at 16-17 mph. On the hills, it is like a giant hand on your back giving you a gentle push. I sweat less on the ebike (great for work) and I average about 30% faster, but it's still an enjoyable workout. As you can probably tell, I am a big fan. You get the fresh air and freedom of a bicycle, and you get decent exercise as well, but at a lower intensity (a legal UK bike will not move at all unless you contribute some pedal power). If you think that fitness is the only reason to ride a bike, then you will probably despise an ebike. But if you cycle for the freedom, the buzz, the low cost, the ability to slice through traffic, and the satisfaction of getting somewhere at least partly under your own steam, then an ebike is a valid alternative - for some people, at some times in their lives.