I have an idea for a show I'd call 'Great and Bountiful' which would chart humanity's first major steps with alien species that don't result in the doctor having to interceed.

While I love Star Trek as an aspiration, I'd actually offer up Stargate as an example of 'humanity gaining access to alien tech and slowly improving'. We know from the lore there is a mass migration to the stars eventually, but humanity in those early years would be great.

One of my favourite shows RTD has done is Years and Years, while I would want a Who show to be that cynical, it would certainly be an interesting take on things to strike that storytelling format.