One thing to add, I've actually asked for people to send me a calendly before, I think that's a good social compromise for everyone- it let's me feel like I initiated the transaction, and overall we still get to schedule efficiently.
This is precisely the problem with Calendly and why I'd never recommend it.
Even though it might seem like the recruiter's time is more important, to me it feels the opposite.
When recruiters ask for my availability, I need to reserve that availability until they get back to me. Often they ask for 3 to 4 slots of time, which depending on the week, might be hard to find, and then those slots are blocked.
When they send me a Calendly link, I can pick whatever slot works best for me and I then only that slot is blocked for me.
I recently went through an Amazon interview round and I had to send them my availability three times because none of the slots I sent worked for their interviewers, which really wasn't ideal and feels like their time was much more important than mine.
For regular meetings though, unless it's my manager or a higher up, I do agree that it feels like whoever sends the Calendly link is in control.
I did like the last approach the most though. Have something like calendly spit out your available times and you paste it into your email message.
They can click on what may work for them. This way it feels like you’ve done some work.
The other thing maybe could be that calendly can generate out your availability in a sentence form that can be pasted in. “I’ve got availability from 10-3 tomorrow, or 10-11 Wednesday” etc.
The point is that you still suggest times in the message but aren’t writing it all out yourself. Keeps it a bit more personal.
In general when someone in a lessor power position tries that, I fill in a bunch of empty times with filler meetings and let them pick from the smaller number of choices given to them.
I like Calendly a lot, it saves a lot of time, certainly more than some more polite scheduling method.
But asking others to find time in your calendar definitely has a power dynamic aspect to it, even if it shouldn't. It's the same as someone asking you to find time in a shared calendar at work (even though that in principle is worse, because the requester could have done the same in that case).
Maybe the solution is a more widely used calendar standard, where you can ask people to share their availability and find a time yourself.
Bottom line, if I was doing any kind of jockeying for power and someone sent me their calendly, I'd ignore it. On a day to day basis, it's easier, but you're showing your lower status vs the requester, even if that's as stupid as it sounds.