I am not aware of diagnostics becoming less rather than more invasive... depends on what you're comparing them to and what you know about the ones perceived as non-invasive that are in reality anything but.
E.g., ultrasound in pregnancy is mighty controversial (and if you haven't heard about it, there's a reason for that... we hear what the establishment wants us to hear, everything else gets swept under the rug... it's just that some of us have stumbled over that rug and developed a habit of lifting it to see what lies beneath before venturing a step.) A fetus is extremely sensitive. Some of the concerns are neurological effects (exposure could affect fetal brain development or neuronal migration, based on animal studies), thermal effects (risk of local tissue heating, particularly near bone), cavitation effects (microscopic gas bubbles forming and collapsing in tissues, damaging molecules and cells), intrauterine growth restriction (observational studies noted a statistical correlation), and subtle long-term effects (concerns regarding increased risks for conditions like autism, childhood cancers, speech delays, etc.). It's just one example, but there are many "non-invasive" diagnostic procedures that are only non-invasive because the invasion is not immediately obvious.
As for insulin -- that was discovered over a hundred years ago... Diabetes, in most cases, could be prevented or cured with better lifestyle and (especially) dietary choices. But the money isn't in that. Hence the current approach -- to pretty much everything.