We always need some amount of goods from our current Age & the 3 Ages previous (most goods from current down to least from 3rd Age removed) for tech tree requirements & CMap (if you chose to negotiate sectors). So, you'll require access to some BA goods thru HMA.
The fan wiki gives (among a ton of other stuff) detailed page for each Age. In that lot is a table listing resources (meaning tech tree) required & lists all goods needed, sorted by Age. If you do Cmap negotiations regularly, then you can click on each sector for its info on negotiations goods requirements.
https://forgeofempires.fandom.com/wiki/Ages
If you've had those BA goods buildings for quite awhile & paid attention to trading to even out the other BA goods, you may potentially already have plenty BA goods in stock for the remainder of your needs. If you think you're short, you could simply use your IA goods to trade down for BA goods (as typically many folks put out 1 good per 2 next lower Age good ratio, such as 15iron for 30lumber - so more return from IA vs BA goods buildings). Or, alternatively, you can use EMA goods traded in same 1:2 ratio for IA goods. Then use those IA goods to trade down for BA goods. Thus, using IA/EMA goods buildings would be much more efficient use of your space than keeping BA goods buildings.