Numerous things. The longer it goes the better the opportunity that some of the info about our debt crisis seeps out to the public.
The MSM isn't going to cover that. They're going to cover the negative effects of the shutdown and blame them on the GOP.
Also, the establishment Loyalists are increasingly exposed and the chance that someone primaries them grows.
The moderate/RINO GOP House members who will end up siding with Senate Democrats to pass a bill with no spending reductions at all don't care about that. They come from districts in which there is little or no threat of conservative opposition, or ones in which a conservative cannot win election anyway.
Finally, it forces the establishment Loyalists in leadership to either move to the right or face the consequences of losing the House majority.
You are making the assumption that McCarthy and the GOP House leadership can control the votes of all of its members. Clearly, as demonstrated by Gaetz, etc.., that is not true on the right, and there is no reason to assume it is true on the left.
The leadership moving to the right doesn't accomplish anything if it loses even a handful of members on its left.The risk you seem to be ignoring - and one that the GOP leadership is
not ignoring - is that it only takes a few moderate GOP members to defect from the rest of the caucus on the shutdown issue. While Gaetz and Co. thump their chest about taking a hard line stand, the Democrats will simply outflank them by pulling in some Republicans who do not support a shutdown.
The result will be the passage of a bill that is much worse than the one that Chip Roy drafted. And as a bonus, House Republicans will being tarred as fractured and ineffective, forcing a pointless shutdown, and that will lose us House votes in 2024.
That is the exact road down which Gaetz is leading his faction, and forcing the rest of the GOP.