They could do this. In fact, in 1979 they did pass the Gephardt rule that essentially states “when we authorize spending, it’s an implicit authorization to raise the debt ceiling if necessary, because we’re not idiots who would tank all US public debt because of a procedural formality.”
Then Republicans repealed that rule in 1995 so that they could use it as a political weapon. Most Republican voters hate debt in all forms, and they have zero understanding of what the debt ceiling represents. It helps them poison-pill any legislation Democrats might pass when they’re in control, whether it’s spending-related or not, whether it’s revenue-neutral or not. It’s not like the filibuster where both parties take advantage of it; it’s really just a thing Republicans do.
That’s why this Kabuki drama of pretending to take a dramatic stand against debt plays so well with the Republican base. They love the spectacle of Republicans threatening to shoot the hostage to enforce minority rule when they’re the minority. People aren’t bullshitting you when they’re telling you that its only de facto purpose is to serve as a lever of power for Republicans. Democrats would love to reinstate the Gephardt rule to avoid all this silliness, Republicans will do everything they can to keep the silliness, because their agenda depends heavily on it.