The idea of starting a game with construction bots and blueprints is great, but how are these 20 very slow bots any help?
I mean they are a little help, but I can - almost - build faster manually.

I would suggest to make a special starting robot (which cannot be build manually), that works like a regular construction bot, but is a lot faster. I believe you can easily do this by copying the data from base game construction bots and only change the speed value.
Then give the player maybe 50 fast bots instead of the regular 20 slow bots, thats something we can work with :)