In ‘Deep Breath’ the Doctor encounters a droid that has replaced so many parts of itself with both organic and inorganic parts that there is almost nothing left of the original. He highlights this with an analogy of a broom only to realise that it applies equally to him.
With his whole body and mind regenerating and changing is there anything left of the original man who called himself the Doctor?
This might be the reason that a limit was placed on Time Lord regenerations. It was not a concern of having a race of immortals but that after 12 regenerations there is nothing of the original left.
Prior to the first regeneration a Time Lord has a body and personality shaped by their genetics and environment. They are a natural part of the universe and regeneration simply extends their presence in it.
Each regeneration make some changes but it is still built on the basis of a real person. The concern here is that what they look like and who they are as a person is completely unnatural.
Just as a paradox can bring information or things into existence within a loop a regeneration creates a person who wouldn’t have come into existence otherwise. Worse still the result of a regeneration could be random, meaning you wouldn’t know who you end up with.
In this light we can understand some of the Doctor’s post-regeneration behaviour from a new perspective. The 5th Doctor’s shifting through former personas, the 6th Doctor’s murderous rage and paranoia and the 12th Doctor’s confusion of identity and simple concepts like bedrooms. All indicate a mind in turmoil, attempting to establish itself. No wonder the 10th Doctor spent so long asleep and emerged with his personality in place.
The telepathic circuits of the TARDIS can help with the formation of the new personality (and may ensure that stored imprints of the Doctor’s mind are integrated). The chameleon arch, rather than being a means to disguise themselves as another species, could have been installed in TARDISes so that their post-regeneration genetic integrity could be re-established. However there is only so much it can do.
If the Time Lords had been allowed to regenerate endlessly their identities would degrade. Who knows how they might have degenerated as a species and a culture? Their eternal life would be meaningless because their original identities would have been erased long ago.
What would it mean for a particularly long lived Time Lord PC? It could mean it is time to re-evaluate their identity. Just as the 11th Doctor realised that his actions meant he was no longer the healer he had named himself for a Time Lord PC might have to take stock of who they are.
They could come to the conclusion that they are the equivalent of a grand child of the original incarnation. While owing their genetic stock and history to them they are far removed and an individual in their own right.
If they feel they’ve drifted to far from the original would they decide that they will be the last incarnation (even if they have some remaining regenerations?) Might they travel back along their time stream to refresh themselves (maybe borrowing some memories and genetic DNA from earlier incarnations)?
There could be consequence for a Time Lord who is so different from his earlier self. It might be that he is different enough that he could enter into his own time stream without ill-effect. His earlier self might not even recognise him as a future version, they are so different.
This could provide the framework in which a Time Lord spends an extended period exploring his own past, trying to remember who he was. All the while he has to hide his true nature from his past incarnations.
In a campaign using the Doctor this can be a good opportunity to do something that couldn’t be achieved on screen and have the 1st Doctor encounter the 12th Doctor. How would such a meeting play out and what would they learn from it?
What if a Time Lord found that his bond with his TARDIS was lost after his most recent regeneration? He is quite literally not the man he was and his time ship now considers him a stranger. What could he do to re-establish that bond?
Enemies as well might not recognise the new Time Lord. Those species that perform DNA scans could recognise that they are the same species as their old enemy but find no other similarity. This may or may not work to the Time Lords advantage.
This works both ways and Time Lord enemies might regenerate into those who could be considered entirely innocent of their earlier incarnations actions or even friends. A scenario could exist in which a good and evil Time Lord swap places after several regenerations.
Just as the Doctor and Clara ponders where the 12th Doctor’s face comes from we might also consider where the personalities of new regenerations come from once they are so far removed from the original incarnation.
It could be that the universe itself imprints upon these fresh minds the people that it needs to exist. If it were lazy they might be copies of existing people in time and space. They could also be hosts for people were removed from time or lost in time scars (such as Clara).
In the Doctor’s analogy it doesn’t matter that the broom isn’t the same as the original, as long as it can do the same job. This can comfort Time Lords experiencing this type of existential crisis.
They might be very different people from the original Time Lord but it doesn’t matter as long as they still have the same goal. In the Doctor’s case that is helping people and saving the day.