Except that Poison, Bio, and Dia are all very potent DoTs. If the recasts on Bio & Dia were adjusted so that a THM could realistically keep them all up full-time, and a resist didn't hose DPS for 40 seconds or so, it would be fine as a DPS, enfeebler, and backup healer.
Whether the FFXI community would accept that or not is still in question, but just because FFXI did things certain ways doesn't mean FFXIV has to. DoT mages are and should be MMO mainstays, including in FFXIV.