The other side of moving the umpire to the offensive side is does he take over the QB when he crosses in front of him? Things like roughing the passer and intentional grounding come to mind. In college with the Center Judge that's what we do.
This discussion seems a LOT more like "a solution in search of a problem". Like many other challenging jobs, being an Umpire, at the traditional positioning, requires training, experience and a certain level of attitude to successfully, and safely handle ALL it's intended responsibilities. There's a wealth of historical advice and documented mechanics available to guide the learning process.
Reality suggests simply NOT EVERYONE is "cut out", nor qualified to be an Umpire (or deep, wing or supervisory (R) official). Given time and experience, most acquire opportunity to sample each position before settling in on a choice. Over time, that choice may change producing teams that are each comfortable and proficient in their chosen duties and responsibilities.
Although we use the same titles at progressive levels of our game, there are SIGNIFICANT performance differences to account and respond to. Differing player talent, complexity, and maturity realities at the progressive levels may well require adjustment and/or modification UNIQUE to each level, that may or MAY NOT be appropriate, necessary or practical at other levels.
Maybe someday ALL NFHS level games will enjoy 7, 8, or even 9 man crews, supported by professional level Instant Review played in weather resistant stadiums on synthetic turf and Game Officials won't dress in girl's Lockeroom's. My crystal ball doesn't reach that far into the future, but God willing another HS football season will start again mid-summer.