"It doesn't fully stop spread, so it doesn't work as a whole". Thanks for giving another example for my comment.
No, they don't. [0][1]
From [1]
> Two doses of MMR vaccine are about 97% effective at preventing measles; one dose is about 93% effective.
Obviously those 3% and 7% do spread, even though the symptoms are milder. For the 97 and 93% ones there's indeed very limited (if any) shedding [3].
Now that's holding different bars, because asymptomatic measles infections are less contagious by themselves, regardless of vaccination status, unlike COVID-19 which is still relatively contagious while asymptomatic. So you're attributing a positive point of measles infections as a fault of the COVID-19 vaccines, which is, as you might see, a pretty misinformed take.
Also, sterilizing immunity as you seem to understand doesn't really exist, in case that's the misconception you have [2]. In the end it's all about viral load, route of exposure, and level and type of immunity. A mucosal vaccine would behave more in the way your expecting intramuscular ones to work[4].
[0] https://academic.oup.com/cid/article/67/9/1315/5034094?login...
[1] https://www.cdc.gov/measles/vaccination.html
[2] https://www.theatlantic.com/science/archive/2021/09/steriliz...
[3] https://academic.oup.com/jid/article/189/Supplement_1/S165/8...