Why four-part stories?

Probably a combination of pacing and costs. Some of the 6+ episode stories could show padding (the last two episodes of The Mutants exist to fill out the run time, and Planet of Spiders has a whole episode that’s an extended chase scene), while doing two or three episode stories while doing 20+ episode seasons would cost more in terms of actors and sets. It’s only when the Seventh Doctor era has 14 episodes in each season that the three episode stories are more common (two three parters and two four parters per season). Even with four episodes a lot of stories wound up having gratuitous escape and recapture sequences, usually in episode 3. Talons of Weng-Chiang has Jago and Litefoot escape via dumb waiter only to get caught again upon escape, just to kill time. Snakedance episode three is basically the Doctor picking up some exposition on the Mara’s origins before escaping and getting caught in the cliffhanger (a notable rare Nysa scream).

Season 12 is an interesting look at this. By framing the season around the Nerva Beacon the sets were used for two different stories. Ark in Space was initially six episodes, but the last two went to what became The Sontaran Experiment, which was shot entirely on location and a minimum of props.

Seeds of Doom addresses the pacing issue by making the first two episodes set in Antartica with the other four on Chase’s estate where the main Krynoid threat is growing. Mind Robber has a very unique first episode that’s minimally furnished, and which was originally allocated as the last episode of The Dominators (five episodes of that is far too many, let alone six!). Fortunately the surreal nature of Mind Robber allowed this to benefit the story, much like when Frazer Hines had to miss an episode.

I'm not sure 4 parters were the default for the entirety of the original run. I remember reading that John Wiles decided to do 4 parters after the 12 part Dalek Masterplan and this was continued by Innes Lloyd for a time, hence the run of 4 part stories in seasons 3 & 4. But those 2 seasons aside, 4 parters don't become the norm until season 13 when the 4-4-4-4-4-6 model was adopted. Up to the end of the Pertwee era, other than the Wiles era, longer stories tended to be preferred on financial grounds in order to spread the costs of the sets over 6 episodes rather than 4.

JNT said he felt 4 parts was the optimum length for a story.

By the time BF started, 4 parts had become Dr Who's default, plus the running time available on a CD made 4 part stories the obvious option on double CD releases.

I'd love Big Finish to do another six-part 'special' release sometime.

Ugh, I meant six  I don't think there's any room on the Big Finish schedule for an eight-part story!

Eh, I think it'd be overkill if it was a six-parter. You can only strech the absurdity so far.

You don't want to strech the joke, though.