This isn't true. No RCTs have ever been performed on the original vaccines and the subsequent variants. And to the extent that other kinds of experiments (retrospective cohort studies, etc.) have been done, they've almost universally found diminished effectiveness against mild illness.

Effectiveness of the original vaccines against Omicron infection, in particular, is essentially zero after a few months:

https://www.medrxiv.org/content/10.1101/2021.12.20.21267966v...

It should be noted that the vaccines appear to remain highly effective against severe illness, even without boosting. The mRNA vaccines, in particular, seem to raise a robust, long-lasting cellular immune response, even though antibody levels rapidly fall. One of the downsides of the unusually rapid approval process for the Covid vaccine was that it was impossible to see this pattern in a randomized trial that lasted only a few months. This led "experts" -- people who really should have known better -- to oversell the shots as a form of sterilizing immunity. They are not.

There are good reasons vaccines take a long time to develop.

From the article I read[1], the nuance was along the line of this -- a person who was previously exposed to the original COVID vaccine or the virus itself (and had an immune response) getting the updated version of the vaccine ends up having the immune response for the _original_ antigen[2], rather than the new one.

Since the immune response is for the older versions of the virus, getting the updated vaccine still ends up having the same effectiveness of the original vaccine.

[1]: https://arstechnica.com/science/2022/02/monkey-study-casts-d...

[2]: https://en.wikipedia.org/wiki/Original_antigenic_sin

Yeah, an immune response specific to the Omicron variant would likely be more effective against Omicron for obvious reasons, but it's probably not possible to get one in people with immunity to older variants because their existing immunity gets in the way. This isn't too surprising - it's one of the things that seems to limit the effectiveness of the flu vaccine.