If you are truly using a utility data model, I would be careful there are many interrelations that could be broken. At this time it may be better to load the full model and just not use the portions you do not need. This model is meant to be starting point for you to expand upon. Potions of these can be removed from your project so you do not need to see them but the underlying data schema should remain in place. Take a look at Utility Network Data Models are just a starting point.
It is a utility data model with multiple pre-populated layers and fields, with some layers already related to others, though no connectivity. Our system isn't too complex on the types of equipment we would like to track so I feel removing all the items that need to be present when publishing would clean it up. Just my OCD/ engineering mentality behind it.
Just something to think about, that I know can occur with other pre-packaged Solutions, and especially since you mention publishing. Sometimes there are already web apps, or other pieces of a larger solution that are pre-built based on an existing schema. If you modify the schema (delete tables and relationship classes) it could break dependencies down the line. This may not be the case in your situation, but is why I mentioned on that other thread that it would be good to work with the consultants to be sure.