I hadn't thought about the relative closeness of Mr. Morland and Mr. Allen based on their positions in society. Thanks for that.

As for the Morlands not being able to introduce Catherine into society, I'm sure they could financially, but it just doesn't seem that they'd have time. We're told in chapter 1 that Mrs. Morland was so busy raising the little ones that "the older ones were inevitably left to shift for themselves". I'd imagine that would be especially true when the required activities involved traveling, such as to Bath.