The IRS probably wasn’t being incompetent here, since they’ve been known to play the long game in cases like this, since the longer someone is delinquent on taxes, the worse it gets when the IRS decides to quit being polite about it.
As a lot of tax cheats have learned the hard way, the IRS has been known to operate by sending periodic reminders that “Hey, you owe us money” for a while and making some effort to collect, but if those get ignored long enough, they’ll simply take a bit of time, build an airtight case, and then slap that person with felony tax evasion charges, which seems to be what happened here.
I agree 100% with you about there needing to be a way to check if a business is delinquent on taxes, especially in situations like flight schools where there may be things like the GI Bill involved.