After whatever point Volvo went to radial tires, 165R15. I don't think wagons ever got radials.

Skinnier tires have less wind resistance than fatter tires. Sounds trivial, but tires are just about the least aerodynamic part of the car.

Skinnier tires and skinnier wheels are lighter than fatter tires and wheels of similar construction, which makes them easier to accelerate and brake. They are also entirely unsprung weight, and less unsprung weight means better tracking over rough roads and possibly a smoother ride. The stock suspension is designed for tires and wheels of the stock weight.

Contrary to popular belief, wider tires do not have any more area in the pavement contact patch than skinny tires -- not more "rubber on the road," in other words. The shape of the contact patch is different, which may cause the skinny tire to wear faster. If there's a handling improvement to be had just from wider tires, it's mostly from the increase in track width. There's not much difference in steering effort either way.

There are not many high performance, high traction tires still available in the original size, whereas there are many more of those in wider widths and lower aspect ratios. The downside to those is that if tires have more grip, they are capable of inducing more body roll than the suspension geometry is designed to handle. So, wider, grippier tires can be just great as part of a suspension upgrade (sway bar and shocks, for a start), but with the stock suspension, they pretty much just mess up the car's original benign handling characteristics.