Please don't waste your energy wondering why kids today don't just exchange phone numbers at age seven. Whatever happened when you were a kid, it's not like that now. Parents and kids all have busy schedules and you have to recognize that. The local kids just aren't out there to be available playmates for your kids. Things just don't work out that way in every neighborhood. And as your kids get older, they and you will find that mere physical proximity does not make real friendships; shared interests--not just having houses on the same street--make friendships. That's why activities can help. Activities are not there just to provide your kid with friends; your kids should do activities that they enjoy for the activity's own sake or your kids will not make friends there. But if they find something they truly enjoy doing, the friendships flow from sharing that experience.
You said your kids lacked interest in activities -- maybe they were in the wrong activities. Let them pick things and ensure that any activity is not (at first) some school-year-long commitment but maybe an eight- to 10-week class through a rec center, etc. -- something long enough for them to build an interest but short enough that, if they aren't into it, they see the end in sight. (If they just love the activity, then sign them up longer-term.)
And don't limit what you and they think of as extracurricular activities. For some folks that just means sports, sports and more sports, but think about arts, dance, unusual sports like fencing or tennis (yes, you can play it indoors in winter), Girl and Boy Scouts, church youth group, Lego build groups (they're out there for kids, try your local library for Lego sessions and Pokemon and other kid gaming sessions!) etc.
Yes, your kids may need down time and not be into doing much. That's fine. I'm just saying that activities can help kids find new interests and get outside their own heads and have something other than school and home in their lives, but you have to help them think outside the box on what activities might be interesting.
If they burned out on previous activities, maybe those weren't the right ones for them, or they had too many. Or maybe you could sign them up for something -- even a one-day, one-time kids' event or workshop at a craft store etc. -- with a friend from school. Ask your daughter or son things like, "How about if we bake cookies this Saturday and you ask a friend over to help us bake and decorate them?" Or, "We're going to the pool on Sunday--why don't you ask a friend to come too? I can ask the parents if you let me know who would be fun to take." Yes, that's being your kids' social secretary, but they are still very young and aren't going to come up with that stuff on their own just yet, and need you to drive them or contact other kids' parents.Plus....doing that kind of thing lets you get to know your child's friends. (And if they say, "Blah, I don't care, there's really nobody I want to ask," push them with a few suggestions and they will end up having a ton of fun.)
You may indeed have to approach the neighbors with kids about arranging play dates. Don't depend on just catching the neighbor kids outside and sending your own kids dashing out to play. Take the initiative and call-- those other parents might be really pleased to hear from you, more than you realize.
Same for parents at school. Do you volunteer at your kids' school or schools? Volunteering puts you into direct contact with other parents who volunteer (and since your kids' ages mean they are early elementary, you are in luck - in those grades, many more parents are volunteering and there are more events etc. that need parent volunteers than in older grades). Get acquainted with other parents of your kids' classmates and then it's easier to arrange play dates. Just seeing parents at pickup and dropoff, is fine if you do that, but seeing them more around school really can help.
You mention that you wonder if you must "be in charge of their social calendar." At least where we live, in an area with many working parents and many kids who are into actvities as well as tough schoolwork, yes, frankly you do have to be in charge of their social calendars at ages like 7 and 8. They can't drive themselves anywhere, the neighbor kids aren't always around as just-run-outside playmates, and they are going to default to "I'd rather just stay home." Home is great much of the time, but also think about whether they might actually like to try something new outside the house.