These hopes were probably based on experiences with "normal" vaccines, which are apt to eradicate diseases through sterile immunity (though there are a bunch of exceptions to this, it's not like we're getting rid of the flu and some other stuff by vaccinations [2]). However, we since learned that a vaccine providing sterile immunity against COVID-19 seems to be off the table (as none of them are), so herd immunity against COVID-19 will likely never be a thing and eradicating COVID-19 is just not possible.
[1] Herd immunity was THE talking point in early 2021 in Germany. Also, remember a few countries trying to get herd immunity by intentionally letting the virus spread (great britain cough cough)?
[2] Sterile immunity seems to be difficult with respiratory diseases (flu, covid, cold, pertussis come to mind). Naively I'd guess that's because the critters have some time to multiply on the surface of the airways and be infectious before the immune system gets a chance to nuke 'em. If that's the explanation though I'm kinda wondering why the herd immunity theory was so common, so it's probably more complicated than that.