You're assuming people aren't lazy. People are lazy and pay a hefty premium on convenience.
Yes, people are lazy. But people are also cheap.
How do convince all auto manufacturers to design internal combustion engines around a certain range of octane/compression ratios?
Wow, that's a red herring if I ever heard one.
In the United States, small cars are looked down upon. I realize this isn't the case in the rest of the world, but Americans in particular like larger cars.
What does this have to do with anything? If anything you're arguing against yourself - larger cars will require larger batteries (and thus multiple battery formats) to travel similar distances.
You also overlook long-term cost
No, I didn't. How did I do that? Short term, you pay less since you are leasing the battery. Long term you pay more since you are essentially paying interest on a loan.
Charging at home will be expensive.
No, charging at home is cheap. Residential rates for electricity are very affordable, especially if the utility offers time-of-use rates. In fact, the Better Place business model _expects_ people to do the bulk of their charging at home!
People who buy energy in bulk do so at a discount. It will be cheaper to swap batteries.
Business rates for electricity are not that different than residential rates unless you're willing to be very flexible with your demand and consume a LOT of electricity. And certainly if you are having to pay a middle-man, you can be sure that that middle man will be charging as much as possible - but you are also going to be paying for the convenience of a battery swap. And you're going to be paying for that very expensive battery swap station. Each battery swap station is going to cost at least a couple million dollars. Never mind that with a 100 mile EV - you're not going to want to stop at a swap station every day or two to swap out a fresh pack - why would you when you could wake up to a fully charged pack every morning?
Cheaper, more convenient, and allows you to drive farther?
The only benefit of a battery swap is that it's potentially more convenient when you want to take long road trips. But in reality, most people do this rarely - those that do will buy a plug-in hybrid instead and utilize the existing infrastructure (their garage and gas stations when needed) for mobility.