Oh, oh ho, no pretty much nothing on this blog comes directly from canon.
It is, at best, things you can infer about canon if you tilt your head and look at it from all the right angles that JKR intended you to look at it.
So, as far as canon is concerned, this never came up. We know muggleborns are looked down upon by your general pureblood wizard, we know muggles are even more so, but Harry’s world is a very small one and it’s never implied that muggleborns have issues securing employment outside of Hogwarts.
Dumbledore tells Harry that Tom ends up a clerk because he wanted to, because he likes dark shiny things. This is despite this having at least been Tom’s second choice in career, something that doesn’t really grant him any power over anyone, and, well, something he doesn’t appear to enjoy in the memories shown to us. But Dumbledore has a boy to convince to kill himself for the greater good and explaining, “And then Tom Riddle, the top scoring student in decades, barely managed to secure employment because of his blood status” makes Tom look less evil. No, all the shitty things that happen to Tom are things he intends to happen! What an evil mastermind!
But yes, for Tom specifically, Dumbledore makes it seem as if Tom specifically worked at Borgin and Burkes because he somehow knew about the sale of the locket. I highly doubt this on every level. I think it made for a nice story that Dumbledore could tell Harry and may even believe himself. Dumbledore, after all, is the kind of guy who thought it made him look fantastic to pretend to light an impoverished muggleborn orphan’s wardrobe and all his worldly possessions on fire to teach him a lesson. HE SURE SHOWED HIM!
The fact that Tom Riddle, who was actively shmoozing Slughorn for years, who supposedly had all these pureblood friends, who had record breaking exam scores, was prefect then head boy, etc. cannot get his foot in the door of the ministry or seemingly anywhere... That’s very very very damning evidence to me.
It also is evidence that makes a lot of sense to me.
The Wizarding World has a hilariously small population. Take Harry’s Hogwarts class size. There are what? About seven kids in each house in his year? Let’s round that up to an even ten. That means at any given time in Hogwarts you have about 280 children. This, even, seems very generous as it seems the important wizarding families don’t have children all that often (once in a generation) and that there might be at most two or three muggleborns in a given year. Hogwarts seems to be Great Britain (as well as Ireland’s) not only premier magical institution but only magical institution.
This seems comparable given that the other major schools we know of cover multiple populous countries in Europe. Beaux Batons, from what we can tell, seems to be the major school for Western Europe. Ilvermory covers the entire United States. Durmstrang all of Scandinavia and Eastern Europe.
I cannot emphasize how small of a population size the wizarding world must be with these numbers. Forget the size of a small country, forget the size of a large city, the wizarding world is approximately the size of a very very very small town.
This is why everyone knows each other, their major shopping district is essentially a single street, their ‘bad side of town’ is a corner on a street, etc. There are maybe a couple thousand people in the wizarding world. This is nothing.
Now, given that, it becomes clear that there just aren’t that many businesses/ventures for gainful employment around. The Weasley twins make their own business, Charlie actually goes to Romania to become a lumberjack er dragon raiser, Bill goes to work for essentially a foreign nation with the goblins. There’s one newspaper and one tabloid that really feels like a newspaper made out of Luna Lovegood’s garage. There’s a series of quidditch teams that feel like it must consist of half the population. Everyone else, if they have jobs at all and aren’t simply rolling in money and being good old lords, works for the ministry.
Now, the ministry is huge, overbloated, and a mess. Arthur’s department, for example, should not exist. How is “Misuse of Muggle Artifacts” such an overwhelmingly large problem that it cannot possibly be absorbed by another department? What this means is I suspect the ministry a) is filled with joke departments nobody needs just to provide jobs b) is filled with coveted career positions c) even if you overbloat the ministry there’s only so many jobs.
Given the world they live in, given the prejudice against muggleborns, do you really think the ministry is going to waste a spot on someone with the last name of Riddle or Evans? Are they really not, instead, going to give that open position to family or friends? The wizarding world feels as if it is made of rank nepotism (Slughorn’s existence even kind of confirms that). Slughorn is so influential because he gets you these networking connections you desperately need. You think Tom enjoys shmoozy cocktail parties with these assholes? You think Lily does? Please, it’s because everyone needs this. The Wizarding World is built on top of who you know.
And, of course, your last name.
Although canon never implies that Lily was anything other than happy to be married to James immediately, have a child, and not work I feel that we’re never given a job for her is very damning evidence. Lily was the most brilliant witch (well probably magic user but I’ll play nice with canon here) of her entire generation, and she either chooses not to get a job or given the above seemingly cannot do so.
I imagine many muggleborns face this bitter reality when they exit Hogwarts. The world is tiny and all jobs go to friends and relatives. Hogwarts was this insular, isolated, dream that made them think they can make it out there.
Even Muggle Studies seems to go to purebloods and the man heading “Misuse of Muggle Artifacts” is a pureblood jackass.
As for Hermione, I think she got very lucky and never realized it. In part because the population is so small, and those who were in power got tied up on Voldemort and thus screwed over because of him, things got very shaken up. More, Hermione by being Harry’s best friend and aiding his quest is a national hero. She gets the leg up she never knew she needed to enter the ministry and earn a very high ranking position very quickly as nearly every occupied position is suddenly vacant from the cleaning house.
Now, Hermione will tell you she earned this herself. That she simply worked harder than everyone else. But she’ll likely never realize that thanks mostly due to her friendship with Harry, as well as being in the right place at the right time, she has the opportunity to do what no one else in her situation could.
But that’s Hermione for you.