Over the years, many ArcGIS users have requested that ArcGIS support allowing field order to be changed on a dataset permanently. One example of this is ArcGIS Idea 1362: ArcGIS should allow the ability to permanently reorder fields in a table.
With that idea being 6 years old and having over 28,000 points, I would try and give Esri the benefit of the doubt and assume that the idea would implemented if it were feasible.
If that is the case, I believe I have an idea which offers a decent compromise - Allow the field order of a Feature Class and Table to be specified within a Layerfile.
Currently, you can specify field order for these items in an MXD, but the field order does not persist after the session has ended.
Layerfiles offer users the capability to save their display customizations of a feature layer to disk. This is why you can add a feature class to your Table of Contents (which is what creates the feature layer), set up your symbology, popups, display tips, label expressions, etc. then save it to a Layerfile (*.lyr), close ArcGIS Desktop then add that layerfile back to an MXD later and all of your customizations are still there.
One thing the Layerfile specification does not support however is Field Order. If it did, I think the need for a capability to permanently reorder fields at the database level would be significantly reduced as you would be able to create a layer file which gave you all of the display customizations and settings you wanted. That's the only place field order really matters in the first place - when its time to display the table.
So if the Layerfile could capture that Field Order configuration and persist it between sessions, and ArcGIS Online, Portal and all of the other client solutions honored it - then, IMHO the need for a capability to permanently reorder fields at the database level would be pretty well taken care of.