This can add background detail to the past of a Time Lord (who may have spent time in Arcadia), used to flesh out the culture of Gallifrey or as a setting for a pre-Time War or post-return of Gallifrey campaign.
We are shown not only Arcadia during the war but some idyllic times before (as the Doctor remembers the children playing). Both make it clear that the people who live there aren’t the usual high collared Time Lords that we are used to seeing.
Arcadia would therefore appear to be where the non-Time Lord population live, particularly since their children haven’t taken to the academy. Their woollen clothes and fabric hats all suggest a completely different culture.
We see a child with a rabbit doll, indicating that toys are part of their culture. It is unclear whether rabbits are native to Gallifrey or if the Gallifreyans are just aware of them and thought it would make a good doll.
The fact that there are so many children is hard to reconcile with Looms introduced in the Virgin range of books, along with the idea that in exchange for an ability to regenerate the Time Lords became sterile.
This could be explained if the average Gallifreyan is very similar to humans, having but a single life and having children normally. This would create a greater division between the Time Lords and the rest of the population.
It raises questions about how easy it is for a Gallifreyan to become a Time Lord. It could be that the Time Lords use looms to create new members of their House, preventing outsiders from joining their ranks.
If a Gallifreyan has an average lifespan then Time Lords have even more of an advantage, since they can live for hundreds of years. The planet would be ruled by an upper class that never changes while the rest of the population is prevented from changing. Stagnation would be inevitable.
It could be that each House or Chapter forces those Gallifreyans who work for them to display this mark. This could be important if there is political intrigue within the capital, to make sure that the person you were speaking to was loyal to you.
If there is a degree of ownership of the lower classes then Time Lords might be responsible for the actions of those beneath them. This can add further complications to the life of a Time Lord PC.
Having two very distinct classes of Gallifreyans, could explain the difference between the Doctor and his granddaughter Susan. He might have rescued her from Arcadia (possibly after the death of her parents). There could have been a social taboo or law that prevent different classes from socialising so they were forced to flee the planet altogether.
For all of this the War Doctor has memories of children smiling so the situation couldn’t have been terrible. The Gallifreyans were still living on the most powerful planet in the entire universe, protected by virtually god-like beings. They might have accepted everything else for the happiness it brought them.
‘The Last Day’ mini episode shows that the walls of the city is well defended, so the city is important. Quite possibly the city is responsible for all of the day to day running of the planet while the High Council in the capital concern themselves with galatic affairs.
It is in Arcadia that the War Doctor leaves his message of ‘No More’ but why did he come here? Why was this the place to leave such a message?
That all depends on whether the Time Vaults are in Arcadia or the capital. One would imagine that the Time Lords would keep the vault close to them but maybe that would be too obvious and so they keep them it in Arcadia. It could also be that you’d need to be a Time Lord to get in and so placing it amongst simple Gallifreyans decreases the chances of unauthorised personnel getting in. The more cynically minded might also suggest that since the Omega Arsenal contains weapons of mass destruction they’d want to keep it far away from them.
If it is in Arcadia then this explains why the War Doctor was there, leaving his message before or after he obtained the Moment. He left it in Arcadia simply because it was most convenient.
If the Time Vault is in the capital then the situation is more puzzling. If it is before the War Doctor stole the Moment it seems an unnecessary delay (unless it is a distraction). If it is afterwards then the Doctor might be taking one final look before killing everyone, which could mean that the place was important to him.
The city must have had some level of strategic value as the Daleks were throwing a lot of forces against it. If the capital was the only important part (and eliminating the Time Lords would pretty much end the war) then this would be a waste of resources.
Could it be that Arcadia is where TARDIS’ were grown? Since they are living things which grow then a non-Time Lord could be tasked with ensuring they provided the nutrients they needed and watched over. This could take several lifetimes for a Gallifreyan, which would be a blink of an eye for a Time Lord.
This all makes Arcadia a way to explore another side of what life was like on Gallifrey. As only its second city there are plenty more spaces on the map to create other locations that can reveal further facets of the Doctor’s home world.