The need to tie the sides together is just part of the real limit on how high a brick (only) structure can go. Even though bricks are relatively "stiff," they still can be compressed by the weight of the layers above.

If they can be compressed, a brick column can bend due to very slight differences in compression on one side vs the opposite side.

If the restoring moment produced by the bending reaches the point where the restoring moment provided by the tensile properties of the structure increases less rapidly than the additional bending moment due gravity acting on the curvature of the structure, one has exceeded the column buckling length-to-cross-sectional-moment ratio, and the structure will fail.

Since brick structures have very low tensile strength, which is the property required for the "long side of the curvature," the actual limit for a straight-up brick structure is quite a bit lower than what's required to "crush the bricks."

It's necessary only to observe that nobody (usually) builds brick structures like smokestacks and such much beyond 80 to 120 feet tall to guess, with pretty good assurance, that anything much beyond that probably doesn't meet acceptable margins of safety using brick and mortar construction alone. Even at those heights, additional reinforcement usually is needed to safely hold things all together when the wind blows.

The widespread use of vaulting, buttresses (flying and otherwise) in large structures made of stone is a necessary thing. Quite a few of the old cathedrals took many years to build, and occasionally collapsed during their construction and had to be redesigned to add compensations for the limited properties of the materials used.

John