Dipoles ideally have 72 ohms impedance. I know most of the time this isn't what one gets and it can vary a lot. But let's assume we can build this perfect dipole that exhibits this impedance.
Why do most designs just suggest a 1:1 balun for coax, if coax is usually 50 ohms? Wouldn't it be better to use a 1.5:1 balun? What would be the loss if we connect a 72 ohm antenna to a 50 ohm line without matching it?
A "1:1 balun" in this application is usually a common-mode choke. Its function is primarily to reduce common-mode current, rather than to perform any impedance transformation.
Such baluns are easy and inexpensive to fabricate, work on many bands, can handle a lot of power, and have low loss; all because in the differential mode they just look like a length of transmission line.
If there were a trivial way to achieve a 1.5:1 impedance transformation additionally, that would be great. Unfortunately there is not. One could use a transformer with an appropriate turns ratio, but that would involve transferring power through the core with associated loss and other issues. Or an L matching network could be used, but again this comes with loss and other engineering challenges.
In practice, any SWR under 1.6:1 is acceptable for most applications. The SWR losses due to such a mismatch are most likely less than the loss that would be introduced by a matching network.
The SWR loss can be eliminated by using 75 ohm coax. Of course the transmitter will still see a 75 ohm load, but this is within the specifications of most transmitters.
In you are feeding an antenna which has an impedance 72 Ohm, you will get SWR:
72 / 50 == 1.44
... which corresponds to ~3% power loss. Considering that the transformer may cause power losses of similar order personally I wouldn't use one.
This being said in reality a dipole can be bent to inverted-V shape. Inverted-V has an impedance about 50 Ohm.
