This looks like a kludge that should be used as a last resort. Transport Stream is not for the Internet.
But yes, working with TS feels kludgy. I haven't had to deal with them in over a decade, but there was one tool that made it all super easy, MP2TSME, that I hear is no longer available
I'm almost certain you've seen some of that output
As a rule, strong feelings about issues do not emerge from deep understanding.