Do I think they should get married? (or rather, the question should be “Should married Catholic priests be expanded, since Eastern Catholic priests and converting ministers from other faiths MAY be married Catholic priests already, albeit rare”) My answer would be yes. While I think there are many benefits to celibacy, the church allowed married priests for the first 1,000 years of its existence, and I think it would be fine to do so again.
Now, would it create a “massive improvement in trust” like you claim? Almost certainly not. It is ironic that one of the reasons that celibacy was imposed during the Cluny Reform Movement was as a reform, because married priests were considered so much more corrupt than celibate ones. Many had families that lived a high lifestyle, and they often engaged in simony, using their positions to obtain good jobs for their sons, sometimes even within the church. This, combined with the demands on their time from the job, caused celibacy to be imposed universally. All it demonstrates is that whether celibate or married, there will be corruption in the church due to our sinful nature, and that we must always be on guard for it.