But why can't it look like a show filmed half a century ago on a budget comparable to the caterering budgets for modern shows? They won't look laughably absurd to modern audiences.
Because it will look old and dated. TOS looks like any other show made 50 years ago. If you remade gunsmoke of Bonanza it would not look the same. Look at how westerns changed by the 70's. You would get something far closer to deadwood in look than Bonanza.
TOS looks old, the tech screams 1960's, the ships look 1960's the cloths look 1960's. It will always look old, because it is old.