I don't have a problem with the spaces inside the Tardis in the Invasion Of Time which are actually a hospital and a London Swimming Pool not a factory.

I see Tardises as temporal repair stations.

They carry a team of Time Lords around the universe to repair the damage caused by their ancestors during the dark time.

It explains the wardrobe of every kind of clothing, it explains the chameleon circuit and why regeneration changes the outer appearance of the Time Lord, it explains the scale of the Tardis interior.

What would that look like?

Well it would require workshops, recreation areas, showers, libraries (basically all the spaces we see inside the Tardis throughout the run of the show).

It has what looks like brick walls on the inside and why not? It has wood grain on the outer doors but they aren't made of wood. The interesting question is why does the Tardis have wood grain on it exterior when it's trying to be a Police Box...? Police Boxes of that design were made of concrete.

Logopolitans aren't computers (though it bares reminding that the first computers in the real world were people) they are processing nodes. Each person carries one data transformation therefore never carrying the full computation. The whole planet is an organic computer (now that is a reference to H2G2).