I've personally tried the self collect blood sample and post to lab process and I don't think it will catch on mainstream. The public would not cope well with the amount of blood they need to draw. I think the yes/no test is a far easier sell, it's whether the government would find the yes/no test results useful or not.
Just checked my NHS app, the one containing your medical records. Its started logging my twice weekly LFT results that I log online. So even though I've only had 1 jab, I still have a valid Covid Pass.