The phrase "the only possible reason" is correct and usable in written English.
You can use it when you are trying to express that the reason you are about to provide is the only one that makes sense. For example, "The only possible reason why he showed up late is because he got stuck in traffic."
The only possible reason would be a huge takeover premium.
He added, however, that hijacking was not the only possible reason for the disappearance.
The only possible reason for this could be to improve conviction rates.
The lack of a quality domestic scene is not the only possible reason international clubs find such favour in China.
"To me, the only possible reason for that is that there is still fire underneath 14 years of smoke".
The only possible reason for restricting religious freedom is when it violates civil law or harms others.
The only possible reasons a Christian could have for not wanting to allow Syrian refugees to enter America are grounded in and constructed out of fear.
In our experimental settings the only possible reasons for deviations from Hardy-Weinberg is sampling error (limited population), selection and non-random mating.
They may rather be seen as the result of an automatic global reasoning to fill in gaps between observations on node variations, in order to find the only possible reasons for such observations.
Chemotherapy remains the only possible option and for this reason the identification of molecular events underlying TNBCs and breast cancer metastasis is needed to develop an efficient therapy.
In both cases, he claimed to give unreserved expression to the new and rare (nova et rara) in propagating what was for him the only possible form of life: that of processive reason or of processes directed by reason.
