How will the bus cost more than £1-2 per 15 minutes, are buses very expensive in the UK, or are you just not spending very much time at these stores?

I will say, that sounds expensive for parking, but completely not out of line with what I would expect to pay for premium (location) parking, though I'm used to VHCOL parking rates and maybe you don't live in that big of a city.

Given the choice between the shopping center with convenient parking and taking the bus downtown, the shopping center still wins.

This is in London, not in the main center but about halfway out.

£1.85 each ride. So £3.70 round-trip.

Or just drive directly and quickly for pennies of electricity and free parking in a shopping center.

Yes I think that was parking cost not bus cost they were talking about (buses can be expensive for short journeys but the cost usually doesn't rise that much for longer ones in my recent experience - I paid £3 for a 40 min journey last week. But bus fares were capped at £2 for ages so I don't have a good feel now for what they cost).

Parking in premium areas can certainly be £5 an hour - but that really will be for premium areas with few spots and high demand, although that's a common situation in historic town centres. I wouldn't be mad enough to try and park in London but I'd expect parking there to be through the roof. The places I usually park for shopping etc (outside London but still SE) are more like £1 an hour in town centres, or free when the car park belongs to a shop or is in a less on-demand area.

In cities with good public transport few people take the car to the city center, yet the shops are dead. There also hasn’t been a major reduction in parking over the last couple of decades that would explain the phenomenon.

What do you mean no major reduction? You used to be able to park for free to pop into a shop to quickly grab something, now you have to pay high rates via an app and you are fined automatically via CCTV if you run out of time. That did not happen a few decades ago.

Or just go to a supermarket or shopping center where parking is free and easy

That is not the case where I live but the shops are not doing well.

That's the crux of it. Most places outside of London don't have good public transport.

I can catch a bus but I have to walk to it, it comes at most twice an hour (usually hourly) and it a very circuitous route so it take ages.

Or I can drive 15 minutes from my door but it's expensive to park. So I generally head in the other direction to an out of soulless town shopping centre.

It would be luxury to have something like the Tube arriving every 2 minutes. I love it when I'm in London.