Actually, I have to disagree with this assessment. One of the reasons why I thought Lazenby was right for this particular Bond movie was that he portrayed Bond as a human being, instead of a cool and distant superspy.
I agree Lazenby shines in some "human" moments that would have much been more difficult with Connery. For instance, there's the scene where he strangles a foe with a ski and tries desperately to do it quietly enough that the others won't find him. Here, Lazenby manages to get across a genuine fear that, for me anyway, is very Fleming-Bond and very un-Connery Bond. But in the scene where he proposes to Tracy, he is -- again, for me -- as uncomfortable and awkward as a teenager playing a love scene in front of his assembled classmates in a high school play. Although I suppose you could argue that, too, could be "human" and endearing if you go in with the right attitude. In a sense, it's kind of sweet that Mr. Expert-At-Everything would seem so awkward and at-sea when it comes to expressing genuine love for the first time. What I call shaky acting one could charitably explain as the character's nervousness.
I will also agree with you that as iffy as the scene is for me, it's even harder to imagine Connery pulling it off. It's a two-sided coin: on the one hand, Lazenby as the "human" newby is able to do things the seasoned pro/Superman Connery would have had a much harder time selling. On the other hand, it's this very human-ness that made it so easy for audiences to dismiss it all as "not really James Bond."
Where it would have been nice to have Connery is in "pay-off" scenes like Bond throwing Moneypenny his hat one last time. But in the end, I think his presence would have resulted in a very different film, and ultimately probably not one as remarkable or memorable.