Jobs' statement at the time was the intent to make it a published standard. If that standard was patent encumbered (or could be claimed to be, as the suit did) then it would be pretty hard to convince other people to implement that standard, and difficult to get a standards body to actually publish it. Why would Google, MS, or anyone else implement something if it'd get them bogged down in the same lawsuits Apple was already dealing with?

There's lots of standards covered by patents. Gif included https://en.wikipedia.org/wiki/GIF

Yes, which is a great example of a patent encumbered standard creating problems for people implementing the standard.

Considering FaceTime postdates the GIF experience, I'm sure plenty of corporate lawyers understood the problem much better.

As a matter of policy, I avoid looking into details of patents, but from the title, I thought the patent was about something the server does, routing or something? In which case, infringement or licensing would scale with the number of users, not the number of shipped clients.

This was around the same time that Apple was charging for OS upgrades, at least on Mac, and I think they wouldn't have wanted to pay for something they were providing for free.

Making the protocol a standard doesn't mean they have to accept every client. They already restrict that.

Making it an open standard and then not accepting any clients but their own is an option I didn't even consider.

Not sure it would help them build their network, but I guess it's an option.