It's a category. All lines are arbitrary to a degree and "interbreeds and produces viable offspring" is not exceedingly arbitrary. You can have arguments around populations which could and would interbreed if they weren't geographically distinct, you can argue about whether offspring needs to be viable no matter which way around the sexes of the parents are, or how large the percentage of viable offspring needs to be, but in the end, yep it makes sense to have a distinction somewhere around that bunch of criteria.

House cats and European wild cats are considered distinct species not because they're genetically incompatible, but because they don't interbreed to any significant degree -- too many behavioural differences, and we're not speaking about culture, here. So even if they could intermingle in theory in practice they don't, so they stay separate, so they're different species.

It's kind of... a behavioural view on the genome? If you have a better idea, field it, there has to be some dividing line because taxa for the taxonomy god.