The Betz limit is based on an extremely crude model for an actuator disk. If you want to compare the performance of the product of a billion dollar industrial development program, let's at least use a respectable benchmark.
Image lifted from: Ideal Optimum Performance of Propellers, Lifting
Rotors and Wind Turbines - https://openscholarship.wustl.edu/cgi/viewcontent.cgi?referer=https://www.google.com/&httpsredir=1&article=2174&context=etd
See eqs. 46,47,48 for a comparison of Betz's ideal spanwise circulation vs the Galerkin ideal spanwise circulation.
Accounting for profile drag (and possibly a tip factor) yields the following graph for an infinite-bladed rotor.
So the reality is that for an ideal rotor in real air that creates a uniform wake around the entire cylindrical shell at all radii from hub to tip, accounting for profile drag, induced drag, swirl, and real tip vortex core phenomena, The optimum power coefficient is about 0.55 at a tip speed ratio in the five to six range.
A three bladed rotor can't produce a uniform wake because some of the air in the swept disc never gets very close to a blade. For example, take a 95.5 foot diameter turbine with three blades. Along the perimeter of the swept disc, the tips are 100 feet apart, so in the middle, the air is fifty feet from the nearest tip, yet it is scored in the swept area.
To understand what is going on, change you point of view to a stream tube flowing downstream behind the turbine. If the tip speed ratio is 5, the blade tip travels 5 feet for every 1 foot of free stream wind movement. So the blades chop the stream tube every 20 feet. That's a lot better than 100 feet. And when you account for the wake induction and deflection, it is less than that. So a stream tube has an infinite string of blade wake vortexes running downstream about 20 feet apart. When you integrate this half-infinite string of vortices to get the wake's real velocity profile, it ends up being pretty smooth over the entire wake. The vortices from far down stream have a significant smoothing effect on the overall wake.
Having said this, it is still better to have smaller vortices closer together than bigger ones further apart. And we can see that the tip speed ratios of real machines are designed to be a bit higher than the ideal tip speed ratio. This helps with efficiency and it helps with the mechanical gearbox and it reduces bending loads on the blades.
Here are two plots of the axial wake factors computed using a pretty good and a very good model of wakes. The second uses a full free vortex model for a long distance downstream.
Images lifted from: A Simplified Free Vortex Wake Model of Wind
Turbines for Axial Steady Conditions - https://www.mdpi.com/2076-3417/8/6/866/pdf