It seems like "American as apple pie" is a more recent American pie identity than I realized! Pumpkin pie was the one identified with the United States more often than not in the 19th century.
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This essay by "L. B. B." appeared in the New Outlook, Volume 24, 1881.
THIS is pro-eminently an American dish. No other people that I ever heard of use it. But so long as the American Eagle and the Stars and Stripes are our national emblems, so long shall we glorify our national pie.
One generation passeth away and another cometh, yet the popular sentiment seems not to be diluted, but rather to grow in strength_ as the intrinsic excellence of the dish increases. I submit that the original “pie of pumpkin", which poets have extolled, would now be considered anything but a dainty dish, and must have borne about the same resemblance to the modern delicacy known by that name as the gowns of Puritan women did to the attire of a fashionable lady now.
I have a friend whose husband used to be always telling what good pumpkin pies his grandmother made. Unlike the traditional husband, he praised his grandmother’s cooking instead of his mother's. But he doesn’t do it now, and this is the reason:
One day there was a guest at his table whose grandmother and his were one and the same person. This cousin was a few years older than he, and had a more accurate memory of long bygones in which they felt a common interest. For dessert my friend had provided one of her delicious pumpkin pies, called so by courtesy, but really made of squash. Naturally the host led the conversation toward his grandmother‘s pies. Not that he depreciated his wife’s skill in that line—except inferentially—but he was especially mindful of his grandmother’s.
Said his cousin to my friend: ‘If Fred had a piece of one of her pumpkin pies now he could not swallow a mouthful of it. She made them very thick with pumpkin, sweetened them with molasses, and flavored them, if at all, with allspice."
“But you must admit, Amelia," said the discomfited gentleman, “that grandmother’s pies were good for those days."
“Hardly so much as that; for she was the plainest of plain cooks even then. But you used to call there coming home from school, hungry as a bear, and no doubt her blocks of pie tasted good; but they wouldn’t now."
That is precisely to the point. “Hunger is the best spice,” and though the primitive pumpkin pies were doubtless made according to the above simple formula, our ancestors relished them because they could get nothing better; but if one of them could step out of his picture-frame some day, and dine at the family table, he would scarcely recognize the pumpkin pic of the period as being in any degree related to his old favorite.
Alas! that the requisite skill to make these best of all pies is not universal in the land, as witness the flabby, insipid specimens seen upon so many tables. it must be chiefly for its name's sake that people continue to use the old coarse-grained pumpkin when squashes are so abundant, a thousand times better, and more easily made into pies; for squash enough for a dozen can be stowed in a few minutes, while it is a half day's job or more to stew a pumpkin.
“The longer it is stewed the better it will be", is the old theory ; but squash is not improved by long cooking. Those which are too moist for table use are the kind for pies. Stewed squash can be kept for a week or more in a cold place, and is convenient to have all ready to make up. A teacup of the strained squash and an egg to a pie is the rule; but at the present price of eggs they seem to go further, and two for three pies will do very well, and you would hardly know the difference. Cinnamon and ginger are the only spices needed—enough of both, especially the former—a little molasses for color, and. a good deal of sugar—the amount can only be determined by tasting, and “ a little more " is nearly always needed. The remainder is all milk, the richer the better ; but if last night’s milk is used, from which the cream has been removed for coffee, it will scarcely be missed. Now what can be simpler to make than such a pie ? And yet in perfection it is the very poetry of food, and fit for a king's table.
Of course the crust is a factor not to be overlooked. It should not be thicker than the under crust of other pies, though it used to be thought otherwise, and that any degree of toughness was allowable for pumpkin pies. Happily, in these days, the kind that we have to exert ourselves to cut is not popular.
But the filling is the principal thing; above all, let there be enough to fill the dish, without having a battlement of crust to guard the edge and hinder approach to the riches within.
The baking is also important. An underdone pie, especially at the bottom, had better never have been made. No rule for the time required can be accurately given; but a slow bake is the best, which will require about an hour.
When done "just right," cutting the pie will scarcely soil the knife, and the cut places will have a sort of granulated appearance. This, if other requisites are not wanting, is a pretty sure test of a perfect pumpkin pie. Tastes differ, but I have yet to see the first person that does not like this kind.
It seems like "American as apple pie" is a more recent American pie identity than I realized! Pumpkin pie was the one identified with the United States more often than not in the 19th century.
Being excessively hard, beautifully mottled with dark and light brown, and capable of taking a very high polish, they are extensively used by turners for making the handles of bell-pulls, napkin-rings, the knobs of walking sticks and umbrellas, humming-tops, rosary cases, and such like.
Of the nut are made vessels of different forms and uses. When preserved whole, and perforated in one or two places, the shell serves to carry water, and two of them are suspended from opposite ends of a stick. 
