Put in simple terms, the reason you should get an electric bike is because it's good for you. Not good for you in an eat-your-vegetables kind of way. It's good for you like few things in life are. The kind of good for you that's a lot of fun.
While it's true that it's more work to pedal a non-assisted bike, it turns out the extra assist means people go faster and ride longer. The difference in intensity isn't all that much either. When Brigham Young University put together a study comparing electric bikes and conventional bikes, they saw only a modest decrease in heart rate. When doing the same 6-mile loop there was only an average 10bpm difference between the two types of bikes.
Not only is there not much difference in intensity when using an electric bike but you don't need to be riding one for long to see improvements. A study from the University of Basel showed that just 4 weeks of three days a week commuting was enough to start seeing progress.
It's not cheating to ride an electric bike. It's going to get you fit and it doesn't take long to see improvements. If that's not enough motivation, it's also worth noting that it will probably save you money to ride an electric bike.
Cars are expensive. They are expensive to buy and expensive to own. Even if you don't count the cost of the purchase price of your car you still have to pay for fuel, insurance, and maintenance. That all adds up and it adds up to a lot. The purchase price of an electric bike might seem like a lot but if you can trade car rides for bike rides you stand to save a lot of money.
Buy an electric bike to get healthy, have fun, and save money. That's the most classic sales promise in the world but electric bikes deliver.