The coax connection is technically not a short, as the path still has to go through the transformer. Also, a 49:1 balun has a different number of turns for primary and secondary windings, where an isolation transformer has the same number of turns and is similar to a 1:1 balun. While an isolation transformer may reduce common mode current, it will not correct the impedance mismatch the 9:1 or 49:1 balun is designed to fix, and it may not have the power carrying capacity of a balun designed for transmission.
Additionally, some balun designs use two or three wires wound around the core together, with the coax shield connected to one of the wires on both ends. Removing one of these connections would effectively remove one of the windings of the transformer. Removing what you incorrectly see as a "short" does not turn it into an isolation transformer.
You can run an end fed antenna without an impedance transformer, but the result is a large impedance mismatch that must be dealt with. See What is the impedance of an end-fed half-wave antenna?
A common half wave end fed antenna is the J-pole or the end fed zepp. This antenna uses a quarter wave open wire transmission line as an impedance transformer. The transmission line (of any impedance) is shorted at one end (Z=0) and open at the other (Z=infinite), and a feed point is placed in between where Z=~50. The radiating element is connected to one side of the open end. The J-pole typically has a separate 1:1 balun, but this isn't strictly necessary. (An effective "air core" balun for this would be 5-10 turns of coax bound in a coil.)