Better than a form plus a spreadsheet
The difference is where the truth lives. A form and a spreadsheet each hold a version of the list, and keeping them in agreement is a recurring job with no deadline and real consequences when dropped. A registration page keeps one list, capped from the inside, and the personal links are issued from that same list.
This is exactly what My Joyfullday's webinar invite does, and it applies to online gatherings well beyond the word webinar. If the event is online, has seats, and needs people to be reminded, the shape holds: a page for the promise, a list for the names, a link each, and reminders before the hour.