I can see, and largely agree with, your argument, Mike. The modern narrative is very much that Christianity consciously and actively usurped existing rituals and festivals, where there was more likely a bit more "give and take" than that.
Like any folklore or myth, the stories will have cross-pollinated with one another, with the beliefs of one group mingling with the beliefs of another as societies spread out, interact with one another, and share stories. A story told to Group A changes when told to Group B, to better reflect that group's preconceptions and shared experience. On a wider scale, that means Christianity borrowing a little from paganism, paganism borrowing a little from Christianity, and so on. And not just Christianity, but any religion - pretty much any religion of Indo-European origin can trace its roots back through shared stories and ideas, and it is an oversimplification of the spread of culture and the diversification of belief to claim that one religion "stole" or usurped a story from another.
And, of course, there are set times and dates that will carry religious significance almost universally - there should be nothing surprising in agrarian societies placing a great deal of importance on harvests and equinoxes, or in seeing the winter as a time for restraint and austerity.
Then there's the fact that an awful lot of "pagan" British traditions are in fact rather modern inventions - the earliest references to Morris dancing date from around the 1400s, so the notion of it as a pre-Christian pagan tradition doesn't really bear up to scrutiny.
I do have some sympathy for
@escargot's point, though - with Christianity as a state religion, there is of course a little more agency than the natural intermingling of cultures, though there's a difference between the religion you state you believe in and religion as observed; I'm put in mind of South American cultures mixing South American and African religious beliefs with Christian iconography, as they rationalise their existing traditions with the "new" belief system brought to them by missionaries, or of different culture's flood myths being reconciled with the Biblical account, which again is an example of two cultures borrowing from another and their stories changing as a result, though there's a power imbalance when Christianity has a state backing.