You definitely don't need to (and shouldn't!) go as far as Japan, but even in places with abundant space like America or Australia, there are huge advantages to keeping homes relatively smaller in terms of land-area per-person. (Floor space can stay higher by: building multi-storey row houses, building apartments, reducing private lawn areas, etc.)

Keeping things less spread out is much, much more affordable. Fewer roads to maintain, fewer ks of electricity, sewerage, and Internet infrastructure, etc. It makes public transport run much more efficiently, which reduces the cost of operating it, which means you get more of it. This makes it a better service, which means people use it, which takes cars off the road, which makes congestion less of a problem, which makes getting around faster. Ditto the cost and usability of bike paths and nice pedestrian footpaths, which become more usable as a result of things being literally closer together, resulting in a store you might once have had to drive to get to being possible to walk to now. This in turn makes things more affordable for individuals, because they might not need to pay the huge prices associated with cars (buying the thing, maintenance, insurance, petrol) if they can get around by bike and public transport. Or at the very least, a family can drop down from 2 or 3 cars to just 1 being enough.

It makes housing more affordable, since instead of paying for 300 sq m of land per 100 sq m of floor space, you might now be paying 50 sq m or less of land per 100 sq m floor space. And because things a denser, your commute can drop from potentially over an hour to something reasonable like less than 30 minutes.