I don’t even understand why this is an issue, because TSA screening is funded through user fees. There’s a line item of $5.60 per one-way ticket for exactly this that’s separate from airfare and other fees. ( https://www.tsa.gov/for-industry/security-fees ) If this is so, why does Congress have to fund the program? Why not pass the funds through directly to the agency?
The federal government does not work like a private escrow account where a fee collected for X automatically goes to Y. Tax revenue comes in to the Treasury, and Congress decides what agencies are allowed to spend. So even if TSA screening is funded in part by a per-ticket user fee, TSA still does not get to just collect that money and use it directly. Congress has to authorize and appropriate it.
On a practical level, imagine the chaos if every federal department acted as its own tax collector and then set its own spending priorities. That is basically an argument for gutting Congress's oversight of TSA and treating it like an independent agency, just because Congress and the executive branch invented the modern shutdown in the 1980s.
Keep in mind shutdowns are a fairly new concept, that nearly no other country has. The US also didn't have it for most of its history. Congress could stop at any time it wanted.