I agree w/ the other posters as well.
If it’s “family” gathering for a family holiday, most of the time everyone brings something... no matter who is hosting.
And most of the time everyone brings the same thing every year.
DH & I host Thanksgiving, & we provide/prepare/cook the turkey, mashed potatoes & gravy, green beans, roasted squash & apples, mac & cheese, cranberry sauce, deviled eggs, relish tray, drinks, & a couple of desserts. My mom is bringing the dressing, sweet potato casserole, baked beans, an orange jello salad, rolls, & dessert. My sister is bringing corn soufflé, kale & cranberry salad, & 2 desserts.
At Christmas, my mom hosts, & we divide up the dishes similarly. When DH’s mom or his brother & his wife host, we always bring a dish or two.
For family holiday gatherings, the menu gets discussed back & forth, & everyone decides what they’ll bring.
However, for dinner parties, birthdays, & similar events, I never ask anyone to bring anything.
If we’ve been invited to a dinner party or similar, I always ask, “Can I bring anything?” And I always, at the very least, bring a hostess gift.
As another poster said, I would never just show up to an event though w/ a dish that’s supposed to be eaten right then during the dinner or party unless I’ve talked to the host... many times, for things like a dinner party (not a family holiday gathering) a hostess has already planned the menu, & an unexpected dish may not be welcomed.
To answer your question, though, if I’m hosting a family holiday & a family member, who was invited, didn’t ask or offer to bring anything initially, no, I probably wouldn’t feel comfortable asking the person to bring something.
But, in both my & DH’s families, I just don’t think that would ever happen. Everyone always asks & discusses - “What can we bring?”