IRS is run under the Treasury, which yes may be part of the Executive Branch - but that doesn't mean there's 100% support for the current President in every desk. Just like any department, there's a lot of career employees and hold-overs from previous administrations. Just look at the EPA... or FBI.

Not to mention Trump just became president in 2016... they've had his entire life to review his taxes. Wouldn't there be a whiff of something foul, somewhere, if there was something nefarious going on there?

A lack of investigation does not mean a lack of criminal activity. IRS is perpetually understaffed and doesn't have the resources to go after HNW offenders, which is why auditing of lower income individuals has skyrocketed

https://www.irs.gov/pub/irs-soi/18databk.pdf

We're talking about an organization that's existing for 96 years... and a person that's been an adult filer for 55 years. I'm confident the IRS has looked into it by now.

Other than disliking the guy - is there any evidence there's any "criminal activity" here?

The IRS audits the president continually, I believe they've done so for many years though I don't recall exactly when they started.

This particular president has been audited for something like 12 years consecutively as I recall. If there were something there to find, it likely would have been found by now.