It's certainly true that the more things child a receives at a time, the more difficult it may be to attribute an adverse reaction to any one of them. Which doesn't support your original claim, that "doing 1 vaccine every few months is less likely to cause risk to the life and well being of the child." Your second argument, that being infected with two diseases at once produces greater mortality, may or may not be accurate (you've provided no supporting evidence), but that's only material if vaccination produces disease. If your contention is that children are at risk of mortality due to concurrent infections caused by vaccination, then please provide some evidence that this actually happens in the real world.
It might seem like I'm unfairly placing the burden of evidence on you by demanding these things, but I need to point out that the U.S. vaccine schedule is determined by doctors and experts in immunology and infectious disease who take this very seriously and who have access to the best data available. If you're suggesting we do something different, then the amount of evidence you'll need to provide to justify that is pretty substantial.
In your last line you suggest that there's a problem with the way this issue is studied--fair enough. Can you explain to me what you think the problem is? I'll point out that the government requires that vaccines be studied the same way they'll eventually be used, so you have kids in group A who get the new vaccine, and kids in group B who get a placebo. Groups A and B will be as alike as possible in all other respects, including the other vaccines they receive. These studies don't turn up the evidence of harm that you seem to think should be there. Likewise, there have been numerous large (as in tens of thousands of patients) observational studies conducted in multiple countries which compare different vaccine schedules, and none of these have identified a smoking gun. So what about the current state of the evidence allows you to dismiss it out of hand?