A car will handle great if you can put the engine and transmission somewhere towards the middle, but obviously that isn't great news for passengers. Mid-engined cars exist, of course, but they're usually two-seater sports cars where space and comfort are lower down the list of priorities.
So you're left with putting the engine somewhere towards the front, or somewhere towards the back. Some manufacturers, like BMW, achieve ideal weight distribution by mounting the engine relatively far back in the front of the car, and putting the transmission and some other heavy bits at the back. This is elegant, but too complex and expensive for your average runabout.
With a front-engined car, you can safely put some of the engine forward of the front axle. Doing so means more space in the passenger cabin, but hanging the weight out front makes the car nose-heavy. In an average front-wheel-drive family car, this isn't necessarily a bad thing, and might even be desirable, as it means good traction and a tendency towards boring, predictable understeer.
Sling the weight out back, like a Porsche 911, and you get the opposite problem: the car naturally tends to want to swap ends in corners. Some drivers find this fun, right up until it kills them. If a 911 is a safe car today, it's because Porsche has spent decades pigheadedly perfecting a layout everybody else abandoned long ago for its tendency to send you backwards through hedges.
Alfa 75’s are along the lines of what you said, but not any of the Germans.
https://www.topspeed.com/cars/car-news/10-rear-engined-cars-...
So the fuel tank and engine could be swapped without affecting weight distribution.
220lbs? Only the lightest ones. Let's also not forget the transmission/transaxle too.
The engine, meanwhile, well it depends what you count as "the engine". If we take it to mean "everything in the engine bay" - radiators, filters, pumps, etc. - you're going to be looking at several times that. Hell, even a battery is like 20kg.
As for why few companies put the ICE engine in the back, whereas front-engine layouts tend towards understeer, rear-engine layouts tend toward oversteer, which is a safety and usability issue for the 99th percentile of drivers (and that's after you put in the engineering to make it work). Porsche spent a lot of effort making rear-engine safe. The design also results in less room for storage.
Also, I'm more than a little skeptical about the frequency of accidents in which a vehicle is launched into the air and rolls over due to the engine being pushed under the passengers.
And even if that scenario is common, I'm skeptical that the risk of that happening offsets the benefit of having an engine between you and a colliding object.