It's less a question of pomp and more of self-image. Ireland and Scotland have been peripheral to the English imagination for, really, the whole history of the Union; why would that change just because we leave?
The English accepted the change in styles that accompanied the Union because of it implied a great enough enhancement of prestige and influence to overcome the inertia of tradition, especially given that, at that time, the Cross wasn't deeply embedded in English traditions, and indeed the whole idea of national flags or even of nation-states was still a novelty; the state and the trappings of state were still conceptually attached to the person of the monarch, and the monarch wasn't changed in 1707 or 1800, just made grander and more glorious. Today, there's no prestige to be found in altering the paraphernalia of state in deference to Celtic secession, and the sort of paraphernalia that the English once wore rather lightly now carries centuries of tradition and familiarity. To accept a reduced flag or name would be to accept reduced national prestige, and for what reason, to flatter a few mad Picts? That's a hard case to make.
