Why are all 3 of propane, butane and isobutane used in deodorant sprays?
Bu/iBu or Bu/iBu/Pr mixtures are easier/cheaper to get instead of pure components as Ivan says, as there is extra effort for their separation, not the extra effort for their mixing.
Butane(Bu)/isobutane(iBu)/propane(Pr) boiling points are $\pu{0 ^\circ C}$, $\pu{-11  ^\circ C}$ , $\pu{-33  ^\circ C}$  respectively. Real boiling points would be higher than boiling points of pure hydrocarbon mixture, as deodorants are solution of active components in volatile liquid hydrocarbons, what increases the boiling point.
Propane (and isobutane too to a lesser extent) shifts usability toward lower temperatures, similar as Pr/Bu mixture of liquefied gas fuel cartridges for outdoor usage. Butane itself does not work well around $\pu{0 ^\circ C}$ either as propelent either as fuel, as it has not enough pressure to overcome the external one.
The goal is to provide the vapour pressure within the given pressure range for the given operational temperature range. Pure compounds have usually too low vapour pressure at the minimal temperature or too high vapour pressure at the maximal temperature.
Another reason is the control of evaporation rate of the solvent when it is being sprayed out. Different compositions of deodorant matrix may prefer different rates of hydrocarbon evaporation and different related cooling effect.