Wire transfers and card transactions are certainly not the same thing, but other than that your post is full of contradictions. You say that I can't use cards to send money directly to someone else. I don't quite understand what you mean by sending money directly...
How do you actually send money to other non-business individual (i.e. small loan to a friend) using debit/credit card? Afaik you could do this 'indirectly', by using 3rd party (paypal, Circle etc).
...and how it is different from wire transfers in this regard, but not only do I see the monies get credited to my bank account (linked to my card) within minutes, I can as well spend these sums immediately
Are you a merchant? If not, again, how do you accept credit card payments? If I wanted to pay you $10 with my credit card right now, how do I do it?
And then you yourself confirm that the recipient accepts payment instantly. How come? Yes, the transactions may get settled some time later, but what difference does it make for me? Further, what's the purpose of chargeback if I can spend the money received this way right away? In the past, I once used chargeback successfully myself, but it was initiated against a company, not an individual...
You don't claim chargeback from individuals, because individuals don't have facility to accept card payments.
From my experience, card txs are not always immediately recorded (already stated one extreme example of tx taking 2 weeks to show in statement). Usually it would change 'available funds' amount immediately (except for weekends) and appear in statement on a later date.
It doesn't matter if bank allows you to spend unsettled amounts. When customer successfully claims chargeback, they would still take that amount from your account, possibly putting you in debt, this won't happen with bank transfers.
Yet further, if merchants are paying for transactions made with payment cards (which may well be the case), why prices remain the same whether you pay with a bank card or through a wire transfer?
Prices of goods/services are the same, but many merchants, or even government institutions (ie DVLA), or airlines, would charge you extra for paying with card (mostly applicable for credit cards). Some won't accept credit cards at all, some would require minimum amount spent etc. Around here, many local newsagents would charge you ~£0.50 for paying debit card etc.