It's honestly funny to me that people think it's so rude to send a Calendly link first than a whole new app was made to solve that sole pain point, https://SavvyCal.com
How does this solve the rudeness angle? I’ve read everything and I can only see that they think their UI is pleasant enough that people won’t mind. Which may be true, but that’s not a direct solution.
I recommend using a "polite" script many people use: "Feel free to let me know when you're available. If you prefer, you can choose from my availability here." It opens the door for the other person first.