In a society with free mages, should we still have templars?

I would rather see the Seekers/Templars returned to what they were under the first Inquisition. Then they concentrated on maleficarum and demons, just as the Fade Hunters did among the Emerald Knights. By all accounts, they were very fair and even handed in dispensing justice and it was likely the nobility who objected to them most because they didn't give them special treatment because of their rank. What was also clear from JoH is that they included mages among their number. Who better to understand the dangers of uncontrolled magic than other mages? So, I do think that some sort of specialist police force is needed but that it needs to be independent of the ruling class or the Chantry. Whether that would be allowed is quite something else. The powers that be didn't seem to like having our own Inquisition keeping order, so I doubt they would look favourably on any independent organisation.

The alternative might be a group of independent mage regulators under the control of the State, similar to how things are managed in Tevinter. There their Templars are just a group of regular soldiers trained to deal with magical offences but without the lyrium addiction to complicate matters. They also have an additional group of enforcers mages, called Justicars, to deal with the really serious stuff the regular Templars cannot cope with. The problem with Tevinter is that there is a degree of corruption that limits the Templars in their duties if their investigations start to tread on important toes. If the Templars were allowed to operate without fear or favour, to the general benefit of the entirety of the population, that would be helpful.

Essentially, you do need someone policing magical offences but only to the same extent as any other crime. The presumption for any mage should be innocent until proven guilty, which on the whole is going to be easier to prove in somewhere like the south where mages are in the minority. If someone has engaged in rogue magic, the list of possible culprits shouldn't be that long and most magic leaves a signature that may narrow the field still further. Since most mages just want to be left alone, I'm pretty sure they would be only too happy to co-operate to ensure the culprit is caught and even assist if their skills allow it.