The US Dollar moved off the gold standard at about the same time as the British Pound. Yet you can still use a 200 year old dollar bill in the US if you so wish (you just can't redeem it at a bank for gold anymore). Of course if you show up with a 500 year old British Pound and try to pay a fine with it, you'll get turned away, but the point is that it's been in continuous use, so I think it's fair to say it's the same currency.

Of course those old coins are practically irrelevant to today's fiat currency, but switching from the GBP to the Euro doesn't just mean "yeah fuck it it's all the same anyway". The currency being controlled by the ECB matters a whole fucking lot because the ECB sets (among other things) interest rates. Recent events should put in perspective how important that is: the ECB's 2022/2023 method for raising its interest rates to combat inflation has been "raise them as high as we dare to while not immediately bankrupting Italy because they have a lot of debt". That's a very real fundamental control that the BOE would be relinquishing by switching to the Euro. Having a currency pegged to the Euro still has those concerns, and also I'm not sure the EU would let the UK do that.

But besides that, I think people do care simply because they like the GBP. Remember that the passport color was somehow a huge thing in the lead-up to Brexit, so I really don't think replacing all those pictures of QEII and KCIII by pictures of fake bridges would go over so well, to say the least.
Even in my country, one of the most pro-European, pro-Eurozone countries, with a previously tiny currency that no-one else used, lots of reactionaries/conservatives STILL think switching to the Euro was a mistake. And everyone old enough at the time will rant and rant about how "everybody" took opportunity of the currency change to jack up prices.

I mean sure, if the British economy falls down so far as to become Eastern European tier, then we might see the tides change. But first of all you still have a long way down to go, and second of all I'm not sure the EU would be willing to welcome the UK back in at that point...