It's just my experience of Doctor Who has been that it's a well of irrational story lines.

There does seem to be an awful lot of arbitrariness involved in the plotlines. For whatever reason it doesn't seem to contain much of the particular kind of irrationality that I personally detest so for me it is just a fun adventure with increasingly pretty girls.

For example why would the TARDIS have a soul?

It is closer to an extremely advanced horse than an extremely advanced car. That doesn't bother me too much. Some of the arbitrary 'rules' of time travel are more burdensome.