Mostly the issue is that Amazon and the likes only give the cashback because they want your data, and Curve doesn’t pass that through because it’s valuable to them as well. It costs a lot of money to run a credit card, and the real reason Amazon do it is so they can know where else their customer’s money is being spent so they can work out how they can get more of a share of the spending. There are probably also the technical difficulties involved and the work would be a) too much to justify on NewDay (the company providing the Amazon card) compared to the gain and b) open up Curve to a flood of potentially difficult integrations for a small number of customers when they could focus on more attractive features.
I get your point about the one card thing. It is frustrating, but in the particular case of Amazon it’s not difficult to just set up Amazon to use the Amazon card and use Curve for everything else. The analytics in Curve aren’t that useful, and on GBIT why would you use any other card on Amazon!?
If NewDay Credit are doing it properly, yes category based spending should be fine because Curve is allowed to pass through the MCC (Merchant Category Code) to NewDay with the transaction, and they should be using this to identify what spending is at restaurants etc. It’s only on specific retailers where it’s an issue, because card providers use the Merchant Name to identify these transactions, and in Curve’s case they have to add the CRV* prefix. It’s the same with transactions routed through the likes of PayPal or other third party providers (including Stripe in some cases).