There are numerous cases of "fully vaccinated" populations having outbreaks, and recent science is showing your assertion about the unvaccinated being the cause of spreading disease to be untrue (at least partially).
Despite high rates of vaccination, pertussis cases are on the rise. Is a new vaccination strategy needed?
https://www.bmj.com/content/366/bmj.l4460
Waning potency of pertussis vaccine a significant contributor to recent whooping cough outbreaks
https://www.sciencedaily.com/releases/2019/06/190610090106.htm
Unfortunately, it's not just dtap, but also the MMR that suffers from the same problem (both are live virus vaccines).
Decreased humoral immunity to mumps in young adults immunized with MMR vaccine in childhood
https://www.sciencedaily.com/releases/2019/06/190610090106.htm
An increasing, potentially measles-susceptible population over time after vaccination in Korea
https://www.sciencedirect.com/science/article/pii/S0264410X17308551
We are also finding the same with the varicella vaccine.
One dose of varicella vaccine does not prevent school outbreaks: is it time for a second dose?
https://www.ncbi.nlm.nih.gov/m/pubmed/16740809/?i=2&from=/16322148/related
So far, the goalposts have been moved multiple times; from needing more than one vaccination after being assured of protection initially (sometimes leading to adult vulnerability and risk of more severe outcomes) to the now oft-repeated claim that the vaccine lessens the severity of the disease (this is brought up when confronted with evidence that the vaccinated actually catch and spread the disease).
What's more, recent study indicates that vaccinated individuals (live virus vaccines) shed and also pose a substantial risk for subclinical infection and transmission).
Asymptomatic Infection and Transmission of Pertussis in Households: A Systematic Review
https://academic.oup.com/cid/article/70/1/152/5525423
Asymptomatic transmission and the resurgence of Bordetella pertussis
https://bmcmedicine.biomedcentral.com/articles/10.1186/s12916-015-0382-8
Now, I'll admit that the MMR and even DTap seem to do well at preventing clinical cases and therefore reduce deaths associated with the same. However, the disease continues to spread and vaccinated individuals actually put others at risk (as noted above). It's also unclear what impact subclinical infection poses.
The potential role of subclinical Bordetella Pertussis colonization in the etiology of multiple sclerosis
https://www.sciencedirect.com/science/article/pii/S0171298515301078
Besides, vaccine efficacy (which is obviously lacking as noted above) is but one side of the coin, the other more important side being what harms are caused by vaccinating? To date we have found problems already (e.g. MMR and epilepsy, polio and SV40) but the sad reality is that quality safety research surrounding "vaccination" is virtually non-existent so we have very little understanding of the risk/benefit ratio as a whole.