I did see a clip of the finale where the kids catch on and, based on what I know of the show, I think they're right: the story wasn't really about their mom. Had that been the case, what would've been the point of Ted starting his story when he and Robin first met?
Generally speaking, because Ted meeting Robin kicked off a long series of events that eventually led to Ted meeting the Mother. The cool thing was that you could look back at several seasons' worth of the show and see that:
"Wow, if Ted hadn't met Robin, then A wouldn't have happened, which led to B, which led to C, which led to Ted being in the right place at the right time to meet the mother."
And it wasn't just about the events that led to them meeting. It was also about Ted becoming the person he needed to be so that he & the Mother were right for each other. And the Ted we saw for most of the last few seasons had grown beyond Robin.
I can't speak for the characters compatibility or incompatibility, but it had been my understanding that Ted and Robin had never fallen out of love with each other
Not really. As I said, we'd been shown a lot of reasons why Ted & Robin weren't right for each other, and they were good ones. They had chemistry to be sure, but they were also incompatible in some pretty fundamental ways, and there were good reasons why they weren't together. And the finale kind of steamrolled over all of that to give us an ending that no longer fit who the characters were.
Also, wasn't it established that the kid's mom had passes away by the time of the framing story, anyways? (I know the clip I saw mentioned that Ted had been widowed for six years, plenty of time to be ready to move on.)
The Mother passing away wasn't officially revealed until the finale, although they'd definitely hinted at it before. And yeah, for the
characters it had been six years, but for the viewers it was about six
minutes. We got the meeting and the happy ending they'd been leading to for several seasons (which was pretty wonderful, BTW), and then we were almost immediately told,
"Oh, BTW, this chick dies after a few years, and Ted's going to get back together with his first girlfriend. Laterz!" So yeah, it didn't really work.