Actually they kind of did (see "BNT162b2 was 95% effective in preventing Covid-19 (95% credible interval, 90.3 to 97.6) below":

"A total of 43,548 participants underwent randomization, of whom 43,448 received injections: 21,720 with BNT162b2 and 21,728 with placebo. There were 8 cases of Covid-19 with onset at least 7 days after the second dose among participants assigned to receive BNT162b2 and 162 cases among those assigned to placebo; BNT162b2 was 95% effective in preventing Covid-19 (95% credible interval, 90.3 to 97.6). Similar vaccine efficacy (generally 90 to 100%) was observed across subgroups defined by age, sex, race, ethnicity, baseline body-mass index, and the presence of coexisting conditions. Among 10 cases of severe Covid-19 with onset after the first dose, 9 occurred in placebo recipients and 1 in a BNT162b2 recipient. The safety profile of BNT162b2 was characterized by short-term, mild-to-moderate pain at the injection site, fatigue, and headache. The incidence of serious adverse events was low and was similar in the vaccine and placebo groups." https://www.nejm.org/doi/full/10.1056/nejmoa2034577

Maybe this is legalese, but I am pretty sure your average Joe online, that reads all kind of weird things on Facebook or other places, won't understand the subtleties of this language.

This quote doesn't say anything about whether the vaccine reduces transmission of the virus. Even large phase-3 studies like the ones done for the COVID vaccines don't have anywhere near the statistical power to determine this. Now we have epidemiological data that shows a clear reduction in transmission, but not as much as the vaccines protect against serious disease.

Here is another quote from the same paper [1]: "This report includes 2 months of follow-up after the second dose of vaccine for half the trial participants and up to 14 weeks’ maximum follow-up for a smaller subset. Therefore, both the occurrence of adverse events more than 2 to 3.5 months after the second dose and more comprehensive information on the duration of protection remain to be determined."

[1] https://www.nejm.org/doi/full/10.1056/nejmoa2034577

Flowchart:

Person A >Transmission> Person B >Transmission> Person C

Person A >Transmission> Person B (Prevention)

This flowchart would be correct if "prevention" referred to "covid infection", but unfortunately it refers to "covid infection with symptoms". Transmission is not prevented, in this case.

well, a vaccinated person supposed to have a 2x shorter interval to spread covid before recovering from it.

The study that you are referring to took place "Between July 27, 2020, and November 14, 2020". The delta variant started in India in late 2020 and wasn't spreading widely within the United States until 2021. It was listed as a variant-of-concern by the WHO on May 31, 2021.

So the research you are referring to is in regards to other variants of sars-cov2

From September 12, 2020:

"A COVID-19 Vaccine May Be Only 50% Effective. Is That Good Enough?"

https://www.npr.org/sections/health-shots/2020/09/12/9119879...

August 7, 2020:

"Fauci says COVID-19 vaccine may only be 50 percent effective"

https://nypost.com/2020/08/07/fauci-says-covid-19-vaccine-ma...

There is nothing about stopping transmission in there.

prevent: to stop something from happening or someone from doing something

https://dictionary.cambridge.org/dictionary/english/prevent?...

In this case the appropriate definition of "prevention" and "what is prevented" is to be found in the protocol of the trial [1], not in a dictionary of the English language.

If I am reading correctly (but do correct me if I am wrong because I am not 100% certain), only symptomatic cases are counted. Hence, it is quite possible for the vaccine to stop the symptoms, but not the transmission between individuals.

[1] https://www.nejm.org/doi/suppl/10.1056/NEJMoa2034577/suppl_f...

Wasn't that the pre-Delta variant(s)?