Transport stream is specifically meant for unstable connections vs Program streams used for DVDs with a nice steady data stream. Digital cable signals and other signals use transport streams specifically because they can resync if things do get out of sync.

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

They are still pretty widely use for HLS/DASH streams. You may not be dealing with them, but you're probably watching them.