What are the advantages of having a road bicycle frame with lower tyre clearance?
It could allow for slightly better aerodynamics and a slightly lighter frame. It allows for a shorter wheel base and you don’t have to worry about toe strikes (toe overlap) too much. It also looks better.
I can’t think of any other advantages. It’s obviously possible to build frames with huge tire clearance without running into great trouble, so it stands to reason that there are very few disadvantages in ample tire clearance.
With very wide tire clearance you run into problems regarding chain line and the front derailleur (hence why most fat bikes don’t have a front derailleur or need some very awkward solutions).