The problem with the future start is balance. You just can’t give everyone 5 planets, 35 pop, and 20 ships. The problem in stellaris with doing this is the randomized maps. Giving everyone an early mid game start with the same resources would be imbalanced due to the map.
Now maybe something they could do is let your empire start off in an AI only mode and run the game as quick as possible (even eliminate graphics and do it at menu level only showing some stats of your would be empire and current year). This is the only way to get a fair and balanced early mid game start when map and players are random in every game (which is awesome for replay ability )
This would be simple if we had console command access, as I am certain you can set your empire to AI control and watch it play itself. HOI4 for PC has this, and I do it all the time to look for AI bugs and mod testing. They even have a screenless way of it playing itself which goes even faster.
For advanced starts, HOI4 has a scenario in 1939 rather than the 1936 pre-war build up years. The problem is balance. Every patch PDS needs to rebalance the entire game and they barely have it half ass balanced for 1936 (which nearly most games are played at based on their telemetry data). 1939 gets no love because PDS doesn’t have the resources so it’s a terrible mode...great idea, no bandwidth to do it. So, in HOI4, to get a best balanced 1939 start, have the AI play itself from 36 to 39 and then take over.
The same concept would be the only way to do it right in stellaris. Hell, just start a game before bed, tell stellaris to stop at a certain year or planet or pop limit, and by morning you will have it. I think fewer people would play this as you think though, because those early years are critical for your success. This would be for those that want to skip the explore stage and most expansion stages all together and go right to exploit and exterminate. Maybe it would keep fans playing who have gotten bored with the first two stages and want the challenge of an unoptimized mid game start.
Considering how little effort it would require to develop this, I do think it’s worth it though.