Here is Meghan's exact quote from the interview in regards to Archine not having a title. She and Harry were worried about Archie not having security. I understand that Archie and Lilli were not entitled to titles at that point.
Do I think she understood protocol at the time? I have no idea because I do not know her. But I do know that if I was a mother and had already experienced years of what the media has done to her, I would have asked for whatever it took to keep my children safe, even if that means creating titles. (I am not saying that she did that by the way)
"They were saying they didn't want him to be a prince or princess, which would be different from protocol, and that he wasn't going to receive security," Meghan said. "This went on for the last few months of our pregnancy where I was going, hold on for a second."
"They said [he's not going to get security], because he's not going to be a prince. Okay, well, he needs to be safe so we're not saying don't make him a prince or princess, but if you're saying the title is what's going to affect that protection, we haven't created this monster machine around us in terms of clickbait and tabloid fodder you've allowed that to happen which means our son needs to be safe." Meghan said no good explanation was given: "I heard a lot of it through Harry and a lot of it through conversations with family members."
One of the reasons why they moved to California is because the state has very specific laws regarding photographing the children of public figures. If they weren't going to get security in the UK because they did not have titles, they may as well take their children somewhere the laws will give them better protection.
As for if they will use their Prince/Princess titles now that they can, I doubt it. No one in the US gives a fuck about royal titles. It is their birthright to use them in the UK though.