Possibly an additional property could be added. This would be that the positional encoding function be continuous and differentiable to ensure the model learns during back propagation. Color charts / heat maps of both the original Vaswani (2017) sinusoidal PE and the Su (2021) rotary PE really help visualize the way the frequency of each input position changes along the model's dimension.
Also, this is the best article on positional encoding I've seen. The way it walks the reader through the subject from problem to final solution in easy to understand steps is fantastic.