There is no "algorithm": the policies of a service like Tiktok are spread throughout its entirety. The only meaningful way to "release the algorithm" would be to release the whole source code.
Furthermore, releasing the source code wouldn't help, since regular people aren't able to understand what it means; and there is no way to verify that the released source code corresponds to what is actually being run.
It would be great if there was some way to verify that a service you're using matches some published code, but we don't have that.
Releasing the code does help. Joe can't open up his car and fix the engine control code, but the local repair shop can and they can also understand it and raise to a journalist "huh this manufacturer pushed a new version that'll make it stop driving if you service it at the workshop of a competitor" or whatever the car equivalent of this tiktok algorithm concern would be
The second problem you mention, I fully agree with: verifying whatever they publish. Client source code, you barely even need because it'll just be a front end for what the servers decide to show you. Verifying that what they say the server code is, is really what the server runs, that's the hard bit. But claiming to be open could be a start; something we can find discrepancies in and push for further openness
Whether this will solve the national security concerns and help with the youth mental health crisis that's often linked to social media, that's all way beyond my expertise and I have no opinion on the matter. Just that, in general, not everyone needs to understand everything in the world for it to be useful to publish
