2 categories are almost empty for curves.
Modify category that is directly relative to object data.
Such modifier changes Normals, UVs and Weight Groups.
Curves don’t have editable Custom Normals, UVs or Weight Groups.
And the fact to add a modifier that is generating a mesh from a curve will not change that those modifiers are requiring such object data from a list like the ones in panels of Mesh Properties.
The other category is Simulate category.
It means Particles and Explosions that have an emission based on indexes of faces of a mesh or of vertices.
Cloth simulation that is requesting weight groups to control pinning, stretching of cloth.
Dynamic Paint and Ocean that has as main or secondary goal to produce textures, vertex colors or displacement.
Fluid that are supposed to generate flows based on closed mesh geometry but also on particles with their emission limited by UV textures.
Most of modifiers of Generate and Deform categories are supported.
About Lacks in Generate category :
Boolean modifier could be interesting but would be confusing.
Boolean operations are actually possible for 2D Curves in Curve Edit mode. So, would this modifier be used for Curve data or generated Mesh data ?
Mask modifier use requires vertex groups or to rig curve with an armature (not impossible because armature modifier is supported but extremely rare).
Multiresolution modifier is currently redone to support sculpting on basemesh with supports of new mesh data like Face Sets.
Skin and Wireframe modifier are generating a mesh from edge data. And curve bevel is already providing a similar result.
About lacks in Deform category :
Displace modifier is displacing mesh vertices according to a texture that is most the time mapped according to an UV channel.
Laplacian Deform requires to define anchors through Weight Groups.
Smooth corrective and Surface deform are requesting to bind mesh data of deformed mesh to mesh data of deformer.
So, missing modifiers are requesting or may make use of basemesh data or derivatives of these basemesh data.
To make them work with Mesh geometry generated by other modifiers, you will need to redesign Curve Object to handle an edit mesh mode by using a basemesh data modifier to store and edit all necessary data, to greyout in UI currently missing modifiers until such modifier is used.
And eventually, you will have to make adjustments to all modifiers to make new system works.
That will be a lot of work.
A lot of that work has already been skipped in an addon like animation nodes that is simply converting a curve object into a mesh one on the fly.
The author of this addon is currently working on making geometry nodes to convert current modifiers stack into modifier nodes.
Whatever you want to achieve, it is probably already possible through addons. And if you are patient ; in several years, you should be able to do it without addons.