With all swords, the very basis for how well a sword performs depends on the blade. The blade dimensions, cross-section, and quality of forging and heat treatment all come together to form a poor, average, or great sword. All other parts to the sword can be changed depending on user preference. However it is not so easy to change a sword blade, which is why some people have multiple style blades for different purposes. Here is a great example of a performance cutting sword. It is the Munetoshi Yuki, which is a hira zukuri blade shape and is meant to cut light targets, especially tatami omote.
It's like using kitchen knives. You would not use a yanagiba sushi knife to cleave bones, and there are many knives made for specific purposes. In translating that frame of mind, why would you use a thick 3 lb katana with heavy niku when trying to perform a double cut or triple cut on tatami omote? It just doesn't make sense. You should use that sword for hard targets like bamboo, or thicker high density targets.
While a thick 3 lb sword does have its place as being a very strong sword that will resist bending, chipping, and breaking, it is a tool meant for taking on armor or high density targets. But no one fights with swords and armor in modern days. This is why sometimes historical accuracy need to be left on the back burner and let modern designs take its place.
Now, let's take a look at the physics behind swords. First, remember that all cutting instruments are basically sharpened wedges. The efficiency of these wedges passing through material depends on the angle/angles of the edge, as well as the thickness. We will leave kinetic energy and momentum constant between both examples to make things simpler.
The illustration below shows slightly exaggerated examples of two Japanese sword cross sections. The one on the left is a thick shinogi zukuri style sword cross section, and has a very scallop-shaped thick edge, also called heavy niku. The one on the right is a hira zukuri style sword cross section and is thinner with very little niku. If both of these swords were swung with the exact same velocity at a tatami target, which would disturb the mat least as it passes through? What about for hard bamboo? Remember that each specific type of sword has its pros and cons in terms of cutting performance, and strength and durability.
So what I'm getting at is the fact that to have a sword that can cut soft targets with the most ease, you should have a thin, light sword. For harder targets, get a sword that is thicker with a thicker edge. While there are swords that can handle most tasks reasonably well, there will never be one sword that can do all. It's just mechanically and physically impossible. But technically, if you're planning on cutting a wide range of targets from soft to hard density targets, then owning a performance cutting sword, a medium weight all-round sword, and a heavy sword for heavy targets will be all the swords you need for your cutting tasks.