It's like my Mum put you up to this to deter me from getting a new bike

So what's a good reason to get a 3k bike? Or even a 1.5k bike?
There are plenty of reasons why one might buy a £3k bike. The number one is sheer pleasure and there is no better reason for buying one.
It's important to understand you will reach a point where a better bike will allow you to ride or perform better. Basically what happens is your abilities are restricted by the bike. In my opinion those who don't agree are flat out wrong. BUT there is no point in using an expensive bike which offers improved performance unless you're pushing yourself in terms of fitness and strength.
You may have missed this earlier. A woman I ride with recently bought the top of the range Trek Emonda. She and I were about equal as climbers. Overnight she began to smash me by 30-60 seconds or more - this is on serious climbs, cat 3 or 4, UK top 💯 s. She's hammering others in the club. We all knew this would happen as everyone could see her potential. The only variable which changed was her bike.
This lady's ability has long been obvious and the Trek has unleashed the potential. No matter how much I spent I'll never get close to her again. Which is fantastic to see.
Quality wheels and tyres will also improve performance and ride. After a quality frame it's the best investment you can make.
I've experienced this myself on my own bikes. On today's ride of 56 miles on my Dolan we only averaged 14.5mph, on my summer bike, Cervelo C3, for the same effort it would have been 16 and if we pushed ourselves 17.5mph.
It must be said winter conditions impact averages etc.