I think doing that means you can find others who are going to do the same thing/others can find you more easily. Particularly for the programmes with like 50 people entering. Knowing people beforehand is always useful
If its a full time job offer, then that's basically standard lol. You can leverage it for other opportunities, happens all the time.
i agree that using your FT offer to leverage for other jobs is fair&wise, but surely it's better to do it in private. email whoever it is you want to work for, telling them you've received an offer and I'm sure they'll fast-track you somehow (ive done it personally, and it works. my linkedin is nearly empty). the way i see it is that if everyone has an offer from a reputable institution on Linkedin surely that decreases any chance of a recruiter noticing you as they have 49 other people with the same job offer in their bio. emailing them gives you a better chance tbf.