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So, we've established that the actual domain name is not a big ranking factor for google. However your chosen domain & site name will feature in your content so I'm figuring it does matter indirectly.

Eg given a choice between:

bobsfidgetspinners.com, welcome to "bobs fidget spinners", we sell fidget spinners....

or

spinnersfidget.com, welcome to "spinners fidget", we sell fidget spinners

I'm going on the assumption that the former is better because it introduces more on-term content (as well as nicer branding). For the limit content that talks about your brand name anyway.

Is this a correct assumption? Would it make any difference if the rest of the site content was on-topic (and good, obviously)?

A year or two ago we put up some websites which were specific to brands we own. Sure enough those sites (eg 'myBrand.com') started to rank pretty well for those brand terms eg 'mybrand curling tongs' (it's not curling tongs, btw, but you get the idea). We were getting a decent amount of traffic presumably from people who have bought or seen these products on our amazon/ebay stores.

Before long, we see us starting to rank well for non branded searches eg 'curling tongs' even among decent competition. Next thing you know I'm getting told by the boss that we need to put up websites for all specific ranges, not just brands, because specificity is a bonus for ranking well.

While there's probably a point that a site for MybrandCurlingTongs lends itself well to ranking for curling tongs, is there also an element that the branded searches we got (via making our brand known on amazon/ebay) helped the site gain recognition and authority? As such a new website about 'ionising hair dryers' would not rank well based on being specific, because it wouldn't be helped by a lot of branded traffic?

I'm removing a bunch of old & rubbish pages and was going to serve 410 to tell google they're gone (my understanding is it'll get them out of the index a bit quicker than a 404).

I should still serve an error page though, right? Similar to a 404. That doesn't muddy the "gone" message that I'm giving Google? There's no need to 410 and die?

A year or two ago we put up some websites which were specific to brands we own. Sure enough those sites (eg 'myBrand.com') started to rank pretty well for those brand terms eg 'mybrand curling tongs' (it's not curling tongs, btw, but you get the idea). We were getting a decent amount of traffic presumably from people who have bought or seen these products on our amazon/ebay stores.

Before long, we see us starting to rank well for non branded searches eg 'curling tongs' even among decent competition. Next thing you know I'm getting told by the boss that we need to put up websites for all specific ranges, not just brands, because specificity is a bonus for ranking well.

While there's probably a point that a site for MybrandCurlingTongs lends itself well to ranking for curling tongs, is there also an element that the branded searches we got (via making our brand known on amazon/ebay) helped the site gain recognition and authority? As such a new website about 'ionising hair dryers' would not rank well based on being specific, because it wouldn't be helped by a lot of branded traffic?