To be fair, I don't think anyone actually does it, because who will do their own bloods, but you definitely can. Labs expect to see an order from the doctor, because that's what 99.9% of people have, but they're happy if you just pay out of pocket too.
The reason I would do it, or do it when in the US is just the convenience. Seeing a doctor is complicated and obviously involves at least one extra step. If you just go and get the tests and have the info, it simplifies things, which is presumably the reason why these direct to consumer options exist in the US.
It's interesting to hear that notionally they have the same model as us of a doctor needing to prescribe the test. The difference in Canada is that private healthcare is not available so you are forced to deal with the public system and the pace and inconvenience that entails.
No, the doctor doesn't need to prescribe the test, you can test whatever you want. It's just that the vast majority of people don't test anything unless a doctor tells them to.
In Ontario the doctor gives me a requisition form with the blood tests they want to do. I take that to whatever bloodwork chain is closest to me, they do the test, and get reimbursed by the government.
I don't think any of those chains have the credit card readers or cash registers to take payment from me even if they wanted to.