Except that if your hypothesis was true, we’d already be seeing 500 deaths a year and we’ve had none (read the article) in the last decade or more.
Therefore, your hypothesis is not true.
What is true is some (note: I said some, not all) kids get sick after they take those shots, it’s just parents don’t put “2 & 2 together”, and you get “unexplained” Sudden Infant Death Syndrome (SIDS) without examining if a recent vaccination may have caused a reaction that led to death. Since the risks of the shots aren’t known in the medical community, the pathologist wouldn’t attribute the death to them, either.
Which is why informed choice is the right decision in this matter.
The percentage of individuals currently in the US that are susceptible (virtually all individuals before 1958 or so likely got measles) and >95% vaccination rates that were present up until 2004 suggests a current susceptible population of only 1% or so. Given that there is no animal host for measles and that the virus was nearly eradicated from the US the rates of measles infections are very low at present the absence of deaths is not surprising... from CDC
Number of measles cases by year since 2010
Year Cases
2010 63
2011 220
2012 55
2013 187
2014 667
2015 188
2016*70
*Cases as of December 31, 2016. Case count is preliminary and subject to change. Data are updated monthly.
In general measles infections have been less than 1 case per million in the US from 1997 to present with 2014 being the notable exception. We haven't seen any deaths but infection rates are in general less than 1 per million at present (0.000001%) not the previous pre-vaccination rate of 1.875-2.5%