The Dashwoods could rent another cottage, if not on such generous terms.

They were looking for a cottage at the start of the novel:
But she could hear of no situation that at once answered her notions of comfort and ease, and suited the prudence of her eldest daughter, whose steadier judgment rejected several houses as too large for their income, which her mother would have approved. (chpt 3).

The cottage used in S&S2 and the description of the cottage in the novel (4 bedrooms and 2 garrets) implies it was of a size equal to the house I mostly grew up in, considerably larger than my own home, considerably larger than the apartment I and my husband shared with my parents for a couple of months on returning to New Zealand without problems, and much larger than the farmhouse my grandmother and grandfather happily raised five children in (and would have raised more if her health had allowed another pregnancy). So a reduction in size by a couple of bedrooms or so does not strike me as intolerable suffering for the Dashwoods, if they did have to take a smaller house if the Middleton's changed.

The Dashwoods' situation may have been slightly worse or slightly better than the Austens' (incidentally, Cassandra did inherit some money from her finance, and the Dashwood girls inherited 1,000 pounds each from the old Mr Dashwood, so they each had some money of their own too). But their situation definitely does not come across as one where marriage was essential for the girls.

The immediate Dashwood family seems to get on very well together. Though Marianne's behaviour is sometimes a trial to Elinor's emotions, she evidently loves her sister very much. We have not seen any quarrells within the family, Mrs Dashwood appears deeply devoted to her daughters and treats them very well. There are none of the stressors that appear in some of JA's other families (eg General Tilney's treatment of his children, Sir Walter's discounting of Anne) that would drive Elinor or Marianne to consider any marriage better than remaining at home.

Finally, though marriage may have made Elinor or Marianne financially better off, it also exposes a woman back then to a significant risk of dying in childbirth. Not a risk to be taken on lightly, and a counter-balance to the attractions of a few more dozen pounds of pin money.

So the Dashwood girls do not have to marry for financial reasons (though a good marriage would make them better off), and their mother and their own relations with each other are nice enough that I cannot seem them being driven to marry to escape a poisonous atmosphere at home.