Being able to schedule appointments online is one of the big wins of modern life imo: it beats waiting around on hold and laboriously explaining to the receptionist how to spell my last name.
I made an optometrist appointment online recently. Their online calendar showed which dates and times were available, so I picked the closest one which was still a few weeks out. I got an email immediately after and a text message confirmation the day before. When I went in at the correct day and time, the receptionist told me I wasn't anywhere in their system and they had no idea there was even an online appointment form. (Yes it was the correct business and they only had one location.)
My guess is that they recently paid for a website which included online scheduling and integration but someone forgot to flip the switch that sent the appointment to their scheduler.
This is not that bad in the beginning (though certainly not good!), the hopeful customer won't be promised anything before the appointment is actually made. If the presentation is sufficiently clear about the appointment hunt not really being over before confirmation it's not that bad. But even when started in a rather benign form, these things can quickly turn nasty, by skimping on the back office and/or "streamlining" the UI into a presentation that isn't clear at all about nothing being committed yet. And I'd also imagine that unscrupulous competition might be tempted to fake-register with the service in some zero-cost tier, effectively black-holing all appointment request to let the resulting Google/yelp/whatever zero star reviews ruin their competition. Which points us to the deepest tier of darkness, the appointment service knowingly claiming to have made an appointment when they haven't, betting on more of the fallout hitting the small business than themselves and using that to coerce them into buying the service (essentially a darker form of what yelp was famous for).
Why the hell no?
At worst "an anonymous form" can ask for your mobile number only to remind you about the appointment (if it's not today for example). At best it should be really optional. In both cases there is absolutely zero need for both a login and a password.
I have a local pizza joint working like that - you just punch in what you need, your number with SMS code confirmation and you are in, with your address/es and pizza coins or whatever. And they have your number to contact you if anything is wrong with the order/delivery.
Another one just asks for a number and call back to confirm with an operator.
Why the hell I do need a login, a password and email|Facebook|whatever for a pizza delivery?
i can make appointments for my country's embassy by picking a time slot and giving them my email address. confirmation then comes by email. no login and password needed.
I'd like to do this there, too. I sorta already do: I use "hide my password" for their website and delete it after the appointment.
In this specific case I was talking about it's even worse: I already have to click a link in the email (or answer an SMS) to confirm the appointment. It's ludicrous.
I 100% prefer to schedule appointments over the phone. That's never gone wrong for me, where scheduling online has gone very wrong quite a lot.