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Thanks for the work, Terri.
Question: Where does your information about Morag MacDougall and Zacharias Smith come from?
How much trust can we place in Rowling's claim of 1:2:1 ratio of purebloods:half-bloods:Muggle-borns? Is this the ratio of Harry's year, of late-20th century wizards in general or what? Much depends on what we think of trends in magical birth rates. Canon states there were over 100 students taking the DADA OWL with Severus (or perhaps those were OWL and NEWT students together?). Canon implies about 40 students in Harry's year though we know the names of 8 Gryffindors, 5 Hufflepuffs, 7 Ravenclaws (including Morag whose House is only mentioned in Rowling's notebook, AFAIK), 8 Slytherins (including Daphne Greengrass whose House is extra-canonical) and 2 students of unknown House. If Severus' year is typical and Harry's year unusual then we can estimate a wizarding population of 8-10 thousands (or even more, depending how many students there were beyond 100 in Severus' year). If Harry's is typical then probably only 3-4 thousand. Even if Muggle-borns have magical ancestors, if those are usually far enough in the past I don't expect events in the wizarding world to influence the rate of Muggle-born births much - not directly in any case. In that case we can assume that for most of the 20th century there were a handful of Muggle-borns born each year, but their proportion of the student body was much smaller in years like Severus' compared to Harry's year. The proportion of pure-bloods vs half-bloods is even harder to determine because of uncertainty about definitions.
Then there is the question of who counts as a pureblood. We know that the child of a magical person and a Muggle is a half-blood, but so is the child of a wizarding-born magical person and a Muggle-born. Are all those of more magical ancestry purebloods or do some still count as half-bloods? If we follow the Nazi-era parallelism then perhaps anyone who has 4 magical grandparents would be a pureblood. IOW Ginny and Harry's children are purebloods, Ron and Hermione's children are half-bloods but their grandchildren might be purebloods if their children marry people with 2 magical parents, even if one or both of those parents was Muggle-born. However if for the purpose of ancestry a Muggle-born counts as a Muggle and that is the reason for Harry to be considered a half-blood then perhaps Harry's children are half-bloods, but it is possible for his grandchildren to be purebloods. Notice that if this rule is applied consistently then the child of a Muggle-born and a Muggle or two Muggle-borns would be considered technically a Muggle-born. In fact it would be possible (though unlikely) for one to have a very long ancestry of many generations of Muggle-borns. Whichever definition is used, it looks like one's lineage can go in and out of being pureblooded over the course of not so many generations. Perhaps some families insist on a longer known magical ancestry. And perhaps having a relative marry into such a family helps 'sanitize' one's own position. We do have Ernie's claim to 9 generations of witches and warlocks (on all sides? if none of these overlap that's 512 magical ancestors 9 generations back) but we don't know about others. Even if the Potters were entirely magical through the line that came through Ignotus Peverell they may have occasionally married Muggles, Muggle-borns or half-bloods on occasion (and it is possible to marry half-bloods multiple times in a single lineage without it ever losing pureblood status). So the statement that someone is a pureblood wizard or witch says very little about hir ancestry. For all we know Septimus Weasley could have been the son of two half-bloods - Arthur would still be a pureblood.
Does it make sense to use such designations? Well, if we consider that wizards live in fear of their world becoming exposed to Muggles then wizards who have regular association with Muggles within their family circle are a security risk. If most families have no more than 3 generations alive contemporaneously then a magical person with a living Muggle grandparent is such a risk.
Question: Where does your information about Morag MacDougall and Zacharias Smith come from?
How much trust can we place in Rowling's claim of 1:2:1 ratio of purebloods:half-bloods:Muggle-borns? Is this the ratio of Harry's year, of late-20th century wizards in general or what? Much depends on what we think of trends in magical birth rates. Canon states there were over 100 students taking the DADA OWL with Severus (or perhaps those were OWL and NEWT students together?). Canon implies about 40 students in Harry's year though we know the names of 8 Gryffindors, 5 Hufflepuffs, 7 Ravenclaws (including Morag whose House is only mentioned in Rowling's notebook, AFAIK), 8 Slytherins (including Daphne Greengrass whose House is extra-canonical) and 2 students of unknown House. If Severus' year is typical and Harry's year unusual then we can estimate a wizarding population of 8-10 thousands (or even more, depending how many students there were beyond 100 in Severus' year). If Harry's is typical then probably only 3-4 thousand. Even if Muggle-borns have magical ancestors, if those are usually far enough in the past I don't expect events in the wizarding world to influence the rate of Muggle-born births much - not directly in any case. In that case we can assume that for most of the 20th century there were a handful of Muggle-borns born each year, but their proportion of the student body was much smaller in years like Severus' compared to Harry's year. The proportion of pure-bloods vs half-bloods is even harder to determine because of uncertainty about definitions.
Then there is the question of who counts as a pureblood. We know that the child of a magical person and a Muggle is a half-blood, but so is the child of a wizarding-born magical person and a Muggle-born. Are all those of more magical ancestry purebloods or do some still count as half-bloods? If we follow the Nazi-era parallelism then perhaps anyone who has 4 magical grandparents would be a pureblood. IOW Ginny and Harry's children are purebloods, Ron and Hermione's children are half-bloods but their grandchildren might be purebloods if their children marry people with 2 magical parents, even if one or both of those parents was Muggle-born. However if for the purpose of ancestry a Muggle-born counts as a Muggle and that is the reason for Harry to be considered a half-blood then perhaps Harry's children are half-bloods, but it is possible for his grandchildren to be purebloods. Notice that if this rule is applied consistently then the child of a Muggle-born and a Muggle or two Muggle-borns would be considered technically a Muggle-born. In fact it would be possible (though unlikely) for one to have a very long ancestry of many generations of Muggle-borns. Whichever definition is used, it looks like one's lineage can go in and out of being pureblooded over the course of not so many generations. Perhaps some families insist on a longer known magical ancestry. And perhaps having a relative marry into such a family helps 'sanitize' one's own position. We do have Ernie's claim to 9 generations of witches and warlocks (on all sides? if none of these overlap that's 512 magical ancestors 9 generations back) but we don't know about others. Even if the Potters were entirely magical through the line that came through Ignotus Peverell they may have occasionally married Muggles, Muggle-borns or half-bloods on occasion (and it is possible to marry half-bloods multiple times in a single lineage without it ever losing pureblood status). So the statement that someone is a pureblood wizard or witch says very little about hir ancestry. For all we know Septimus Weasley could have been the son of two half-bloods - Arthur would still be a pureblood.
Does it make sense to use such designations? Well, if we consider that wizards live in fear of their world becoming exposed to Muggles then wizards who have regular association with Muggles within their family circle are a security risk. If most families have no more than 3 generations alive contemporaneously then a magical person with a living Muggle grandparent is such a risk.