I think you'd be hard pressed to be limited by router power in the sense that most medium to large routers will have enough power for how router planing is typically done, but I think you'll hit other practical limitations more quickly when going for a much larger spoilboard style bit.
The way we use these bits, we are basically taking off a very very narrow shaving along the bottom corner of each blade. In that way it's similar to how a spoilboard bit is meant to work.
To an extent, bigger size is nice because it means a wider swath per pass. So you have to take fewer passes back and forth. Even if the overall operation takes the same amount of time (your passes will likely be slower with a bigger bit) it's just convenient to take fewer passes.
Bigger size also means the speed at the blade is higher for a given rpm. That can become limiting sooner or later in materials that don't like to be cut at high speeds. And, the torque is greater (there's a longer "lever" from the center of the bit to where the cutting is happening). That's an important consideration not just in terms of the power needed, but practically - since more torque means the router is harder to control - it'll want to climb and run from you much more easily. However, since we take off such a small bite, and routers are generally very well guided on a planing jig, it's less of a concern than when doing other freehand routing operations where spinning a big bit is scary. Though, if you're not careful, a router in a sled can still try to pull on you, and personally I wouldn't want to go huge with the bit even if I had the power.
A spoilboard bit meant for use on a CNC machine is a bit of a different animal since you're running it in a machine that doesn't have the same constraints as a freehand router, i.e. you're not guiding it by hand and having to control the "feedback" from the cutting operation by hand. Also, an actual spoilboard, which those bits are meant to cut, is usually a material that's very easy to cut and doesn't fight the way hardwoods can. So a bigger blade isn't really a problem.
A bigger bit is more likely to flex, not because it's more flexible but because of the "lever" effect mentioned above. But as I indicated in my prior post I don't think flex is really an issue with how we use these.
That's a bit of a brain dump on my part. I haven't actually used a bit bigger than the commonly used Freud for router planing, but just having used that bit so extensively, I don't have any desire to use anything bigger. It cuts great and is wide enough to be useful but not so big that it's unwieldy or hard to control. There have been a small number of times where it's size has been close to making me uncomfortable, so I have no interest in a larger bit.