Why? That would that be a ridiculously impractical recommendation (do we even have the capacity to run millions of full panel blood tests a week?) and completely useless for detecting the problems people are worried about. TTS[1] isn’t something subtle you need a blood test for.
[1] https://www.cdc.gov/vaccines/acip/meetings/downloads/slides-...
I just feel like more data is better, the scientist don't seem to understand the mechanism that causes this problem and why it affects a few people but not most.
Your link links the problem to low platelet count, is the vaccine affecting platelets in other people but not enough to manifest the issue? Maybe more data could help figure out why it happened to those handful of people and not others.
The J&J vaccine causes headaches and pains normally , I was down and out for a couple days, I could easily see someone with the issue thinking its normal and waiting too long to go in for help.