Would something as simple as removing the featureclass from the project and adding it back in be sufficient?
No.
Last year we developed our first ArcGIS Server javascript web application. We discovered that we had to use the aliases rather than the field names in the javascript app identifies. Aliases are sometimes changed by the data stewards or may be different between two feature classes with the same field. It would be much easier if we could simply delete all the aliases before loading them in the MXD. That way the field name alias within the MXD layer properterites will default to the field name. Does that make sense?
Must be a quirk of server stuff, if you remove and re-add a file to Arcmap, the alias isn't carried over. Perhaps one of the appropriate web/server forums might address this better.
Alias can be at the MXD level but can be at the GeoDatabase level too. I do not think it is possible to drop them from geodatabase but the easier way will be to calculate them to be the same as the field name. I think this is the default when you create a new field too.