I love this idea. And if a student is having a really bad day, or their dog just died, or they have bad cramps, or they have a hard time dealing with the intense stress of your entire grade being decided in one exam... well, those loser students can just fuck right off.
Accommodations are part of the fabric already. It doesn't seem inconceivable that we couldn't deal with them in exceptional circumstances in a similar way to how it's done today.
... well then, why not use those same protections (proctoring, monitoring, auditing) in continuous examination?
Accommodations are real and necessary, but applied at the end.
(Experimental sciences are an exception)
If they did not do this, they failed the exam on communication with other people.
In addition, we are not always able to make decisions in ideal conditions. We need to learn how to solve problems under pressure, in emotional turmoil, and when we are not feeling well.