Tl;dr I wouldn't attribute it to quill pens at all.
One important thing to remember is that spelling has not always been uniform. Unlike many other languages, English has never had a central authority that decides what is proper English and what isn't; in the early 19th century, Noah Webster decided to overhaul spelling in his dictionary, and because of that Americans still write -ize, -or, -er instead of -ise, -our, -re today (standardize, color, center vs standardise, colour, centre). Even nowadays, it's mostly the creators of spell-checkers and style guides who determine these things, rather than the government.
So if someone was writing a private letter to a friend in the 18th century, our modern notions of "standard" spelling didn't really apply. Some people would try to show off their education by using foreign spellings for foreign-derived words, while others would adapt them to English conventions, and no central authority would declare one of them right or wrong. People were taught "proper" spelling in schools, with the weight of tradition behind silent E's and silent GH's, but the details varied a lot in the edge cases, and even today educators don't all agree on things like "worshiped" versus "worshipped". (I was taught the latter, but that's rare in America.)
And since "standard" spelling was mostly the purview of publishers, private letters weren't examined especially thoroughly. If I want to publish a book nowadays, the editors will tell me whether to use "worshiped" or "worshipped"; if I want to send an email, who cares? The only real difference is that now a spellchecker might complain about one of them, but that's a feature of computers, not of better pens or typewriters. The real difference is that spelling has become more and more standardized over time—but as late as the 20th century, the Chicago Tribune used a totally different set of standards from the rest of America, with spellings like "burocrat" and "hocky". ("Catalog" and "thru" have caught on; most of the others haven't.)
As far as paper being too expensive to start over—back when high-quality writing materials were at their most expensive (the mediaeval period), monks would go to great lengths to erase or correct mistakes rather than letting them stand. And marginal notes have always existed. Later, even on a typewriter people wouldn't want to start over completely unless it was necessary; there's a time cost to rewriting everything from the beginning, no matter how cheap paper gets. It's only in the era of word processors that errors have actually become trivial to fix. So this doesn't have anything to do with quill pens either.