A reason to not run for public office is the damage this may cause for your reputation. You might not ever get a job in the private sector again. Damaged goods.
This also works in other ways I noticed when a befriended journalist joined the elections for a new candidate for a new mayor of Paris inside the party of the Greens. One of his employers called him with the announcement that his contract has ended because of this. You are not supposed to engage in politics as a journalist. The fact that only three party members voted for him did not matter. From a party that only makes a chance when the others leave the race.
If you lose your current job in the private sector simply because you show an interest in running for public office as Elder or minister, this means a large reservoir of good candidates are now excluded.
For this reason the selection of governors should get an adapted procedure. Once they do not come from political parties and apply to the job opening, this selection procedure should protect their anonimity. Applicants should be able to indicate nobody should know about their intention until the last selection round is reached. Only then the identities are revelead from the candidates who chose to remain anonymous. Just before this happens they get the choice to revoke their candidacy. For example because they carefully studied the anonimised profiles of competing applicants. Or they can ask the selection committee to have another candidate contact them to establish among each other who is likely to be the best candidate and who should step back.