Rebuilding a laptop battery pack sounds like an easy endeavour, but getting around the BS rich minefield isn't so easy in practice.
Finding genuine replacement cells of the right size is the first hurdle. Many may use the "18650" others use a "14440" - the numbers are based on metric case sizes... some use a proprietary size, like my HP battery pack built with batteries that look like a squished 9v, but with a terminal at either end. For the usual reasons, China has flooded the market with junk cells with absurd ratings. Any cell rated more than 2500-3500 mAh is likely junk. The last batch I foolishly bought off ebay were rated at 5000mah. Took one cell apart to see why it sucked so much, there was a tiny battery wired inside, and the rest was empty. Genuine Panasonic cells are the gold standard, LG, Samsung, Toshiba and Sony also make good cells. I don't know how to spot a genuine one, price alone is no help, although it's safe to assume a genuine cell won't be cheap. I've purchased batteries from these guys before, and have not been disappointed by performance
Battery Space ... All good, but the price for each cell is much like your $400,000 car example.
Connecting the cells is the next hurdle. They don't take well to conventional soldering, heat from the iron at best will damage parts of the cell like the safety vent or internal electrical bonds, and at worst, cause it to go into a runaway reaction. They need a high current short pulse spot welder.
The last and perhaps most damning hurdle is the authentication, protection and charging board. These are tiny little circuit boards with a multitude of connections and populated with various unlabeled chips. It provides the connection between the laptop and the battery, and also is connected to each cell in the pack for balancing. The board protects the battery from overcharge, overdischarge, and also tampering. Most often there's a chip that acts as a tamper seal, and if it detects anything funny going on, it shuts down the connection between the battery and the laptop. The chip is likely triggered when disconnected from the cells, or when a cell fails, or for any number of other reasons some committee thought sounded good.
In my opinion, building something that delivers 16-18v to the dc input of the laptop is going to be easier than trying to deliver power through the battery connector. However, as you pointed out in previous posts, recharging an external battery isn't that easy, and having to lug it around sucks as well.