Interesting thoughts thanks for that. It makes sense about the much smaller transformers in boomboxes. I don't have any batteries, but I just tried an AC adapter in both my Goldstars - the 800&581 - cranked up the volume with no tape in and pressed play. No mains hum seeping thru the speakers when powered this way as expected. With the mains cord in, the 800 is quite acceptable regarding mains hum, the 581 is awful. So this makes me think the inductive hum I suspected may be a red herring - I think I have grounding issues. This box came with a lot of rust on the speakers and beach sand inside! I've read articles about grounding which have been quite confusing to fully grasp. The main takeaway i took from one article about turntable grounding was that noise signals cannot exist where all grounds (tonearm, turntable chassis, amp chassis, signal ground wire) are at the same potential. Now that makes sense to me. So with a boombox do I have to solder a wire from the tape head case to ground in extremis? I've also noticed with this box that sometimes if I touch the metal tape control keys I get an extra buzz thru the speakers.
My home stack set up is definitely a case of inductive hum however. It's a NAD 3120 sitting on a Nak CR-2 deck. I found only a few forums where this issue is known about and discussed, so it does seem quite rare, but it happens. I'm surprised the manufacturers don't have a warning in their manuals tbh. When you consider that the magnetic strength on a cassette tape is about 24uT and the earth's field at 50deg latitude is 58uT...tape heads are very sensitive.
I've been considering emf noise from cassette motors too. I've seen a kind of shielding tape wrapped around some small mabuchi motors in pics online. I've been looking at these products - might experiment at some stage.https://www.electrosmogshielding.co.uk/product-category/magnetic-field-shielding/ Thinking more about my Nak here as that seems quite noisy even when I eliminate the hum issue by repositioning it. The thing is I don't want to reposition it - there's nowhere for it to go, so I wonder if some mu metal sheets placed between my amp and deck would block the flux?