Why must all magnitude systems have a reference point? Let $f_*$ and $f_0$ be the observed flux of a star and a reference flux in a particular spectral band, and let $m_*$ and $m_0$ be their respective apparent magnitudes. Then the star's magnitude is given by $m_*-m_0=-2.5\log(f_*/f_0)$.
Encyclopædia Britannica maintains that

All magnitude systems must have a reference, or zero, point.

Why is this? It seems to me that one could just say $m_*=-2.5\log f_*$ and move on, no?
Because you can't take the logarithm of something with dimensions only the log of a number.
Your magnitude would depend on what you measured f in. In other words, by choosing a set of units, you choose a zero point! Whether that unit is Jy, W/m$^2$ or the flux of some other object.