The impression that Jane Austen gives about this marriage is absolutely absurd, IMO. (I'm keeping track a little of the absurdities that Jane puts in S&S!) It's taken to extremes in this (boy, wonder what the guy who is writing S&S and Sea Monsters will do with Charlotte and Mr. P!...)

The description of them introduced to the reader in Ch. 19:
Mrs. Palmer was several years younger than Lady Middleton, and totally unlike her in every respect. She was short and plump, had a very pretty face, and the finest expression of good humour in it that could possibly be. Her manners were by no means so elegant as her sister's, but they were much more prepossessing. She came in with a smile -- smiled all the time of her visit, except when she laughed, and smiled when she went away. Her husband was a grave looking young man of five or six and twenty, with an air of more fashion and sense than his wife, but of less willingness to please or be pleased. He entered the room with a look of self-consequence, slightly bowed to the ladies, without speaking a word, and, after briefly surveying them and their apartments, took up a newspaper from the table and continued to read it as long as he staid.

Mr. Palmer didn't marry her because of her beauty. She's "short and plump" (again, the average man does not fall in love with someone because the woman they like is plump - usually inspite of that, or else they are good humored and love her for it -- I don't see that in Mr. Palmer.) Yes, she has a pretty face. That doesn't signify.

Why would a man willingly go into a marriage when he doesn't care three straws for his wife (or much else, for that matter)?

The other idea that occurred to me is that the way he interacts with women, the only woman who would accept him would be a silly, good-humored girl like Charlotte Jennings. The family is respectable, which made it make sense. But again, Jane Austen uses examples in so many of her novels for the absurdity of marriage when a man and woman merely married for comfort, and because they were supposed to. We have this couple, Sir John and Lady Middleton, Charlotte and Mr. Collins, ... (others in other novels? I can't recall, which makes me think she gradually stopped writing about the patently absurd in her later novels...)

An example of Mr. Palmer having a problem with talking with women (and consequently not talking with them) in general. (yes, I know, he possibly can't talk with anyone in general, but we only hear his responses with ladies present, so it's crazy the general assumption he could be a politician who needs to flatter and make friends with his constituent, IMO, too! Unless there is further information I could well not be aware of about politicians in Regency times.)

Ch. 27:

"I thought you were both in Devonshire," said he.

"Did you?" replied Elinor.

"When do you go back again?"

"I do not know." And thus ended their discourse.