I'm fairly sure the original windows were much taller, switched-out, and instead of infilling with mis-matched brick, the wood siding was used. The "too tall" shutters were probably selected to create a transition between the brick and siding below the windows.

While there isn't a significantly good reason to *not* paint brick, doing so often leads to unsatisfactory results. Like wood, brick should be sealed (a clear coat) before painting for the first time. Which is not difficult or expensive to do. Sealing, however, only addresses the outside face of the brick; not it's interior or where it rests on the foundation.

Also, brick is very porous and will absorb moisture from rain and humidity and wick it up under the paint (from the concrete foundation); causing blistering of the paint while allowing unforeseen efflorescence toward the space between the brick and house framing. Efflorescence does not occur quickly and, in most cases, won't be a problem for many years, if ever.

Unpainted brick, however, will dry on it's own quite readily since there's no paint to hold in any wicked-up moisture. Brick homes tend to need re-painting more frequently than wood-sided home. Removing paint from brick is not only *extremely* difficult it *always* damages the brick and mortar in the process. By "damages" I mean, a thin (1/32 - 1/16") layer of brick needs to be removed and the mortar will probably require some repointing.