No they don't.
> "The results suggest even those who are fully vaccinated have a sizeable risk of becoming infected, with analysis revealing a fully vaccinated contact has a 25% chance of catching the virus from an infected household member while an unvaccinated contact has a 38% chance of becoming infected."
A couple of points here:
1) 25% vs 38% is an enormous difference in compounding risk of transmission across populations.
2) Accepting the premise that viral load at peak is the same, multiple studies still show that vaccinations reduce duration of shedding and transmissibility. [1]
> Thus widely vaccinating healthy people, we do increase threat to immunosuppressed and the likes.
This is simply wrong based on above in both first and second order effects. On top of that, having fewer/less severe reactions in otherwise healthy people leaves more healthcare resources for immunosuppressed.
[1] https://pmc.ncbi.nlm.nih.gov/articles/PMC9499220/
https://www.medrxiv.org/content/10.1101/2022.01.10.22269010v...
https://www.gov.uk/guidance/monitoring-reports-of-the-effect...