There are a few reasons for this.
1) Pressure defeats apnea by holding the airway open not by trying to force it back open after it closes. EPAP (exhalation pressure which is the critical pressure for obstructive apnea) applies enough pressure/force to the inside of airway to prevent it from collapsing. EPR/PS primarily affect flow by increasing pressure differentia, his helps in cases of partial restriction such as hypopnea, flow limited breaths etc.
2) Backup rate is mostly used in cases of neuromuscular disorder or central apnea. In neuromuscular disorder cases it can stabilize the breathing rate and keep breathing effort in sync. In central apnea it can kick start spontaneous breathing and if you use high enough PS (and especially high variable PS used in treatments like ASV) then you can supply large enough pressure differential to force a breath even if your body doesn't spontaneously breath (acts like a ventilator in this case).
3) The reason backup rate isn't used on all machines is because it is invasive and because in order for it to be effective it has to be timed closely to respiration rate which means it can get triggered in cases it is not required. Another reason it isn't used is because in order for it to be effective you also require that the pressure is held in an increased state for a period of time (this timing control is called Ti min) which again is invasive and alters your spontaneous respiratory drive in say rem sleep where your breathing naturally has some odd short breaths.
So long story short backup rate affects your spontaneous breathing effort and therefore is not ideal for the majority of basic apnea cases. If you are having apnea you need to determine if they are obstructive or central in nature. If obstructive in nature the treatment is to stop the apnea from occurring before it happens not to try blast it open after it happens, this is done by increasing EPAP or by treating positional apnea with a cervical collar etc. If central in nature you may need backup rate but you also probably need variable PS which means you need an ASV machine which is too invasive for most basic apnea cases.