Actually, there are two downsides.
1) Settlement happiness is improved by "non-essential" furniture (everything except beds), and objects in the decoration category, so scrapping them all will negatively impact your settlement's happiness, and therefore, your settlers' productivity. If you later go to rebuild these types of objects to improve happiness, they will cost more in resources than you got from scrapping them.
2) At least at present, on the PC platform, I've noticed that the contents of many containers (and corpses, and so on) undergo a respawn during the Act 1 -> Act 2 transition. So a little less loot too.
The cutscene where the BoS fly in and announce their presence to the Commonwealth over their loudspeakers indicates that you have entered Act 2. So, the transition would be opening the door and stepping back into the Commonwealth from Fort Hagen after killing Kellogg and completing the Reuinons quest.
Pretty minor downsides, but there they are.