In practice that would create even more ineffective veto points that already result in stasis and dysfunction in the US Congress.

For more than a decade the US has been stuck operating by renewing the same budget more or less with minor modifications at random intervals of time depending on the political mood. It always gets approved eventually after occasional pointless, wasteful shutdowns. But nothing actually changes from those veto points, just more routine dysfunction and grandstanding.

Same with debt ceiling. Another veto point that gives leverage but has zero effect on actual spending. It probably sounded like a brilliant idea to control spending in the 70s or whenever it originated. But is entirely ineffective at the purpose of addressing the deficit.

Self expiring legislation would very likely end up the same way. Just another pro forma procedural roadblock that wastes time and makes the legislature even less effective at real problem solving instead of posturing.