The banks which the government bailed out in 2008 have repaid almost all the money. £33 billion still remains to be paid, and probably will be. By extending credit - something only the government could do - the government stopped a huge collapse which would have cost the UK much more. It was worth doing.
The government also paid out billions to stop companies collapsing during Covid Furlough. That cost £70 billion. Much of it will never be repaid (unlike the bank bail outs), but despite that, it was still worth doing.
You really are missing quite a big chunk of understanding if you think we'd be better off without investment banks.
At it's simplest, without financial markets, companies wouldn't be able to take investment money from peoole who are willing to defer their spending (eg people saving for their pension) in order to invest in things like machinery which hugely increase their productivity. Companies being more productive means they are able to employ people and pay taxes. The taxes on all the extra stuff they make pays for hospitals, schools etc.
Without it being a market, those pension savings wouldn't be funnelled to the companies who can make best use of it. Ie have the biggest improvement in productivity for the amount of investment available. And hence pay the most extra taxes on the extra stuff they make. And get the most money into hospitals and schools.
Without currency and interest rate instruments, companies wouldn't be able to fix costs when fulfilling orders for customers abroad or eg a year in the future (to give time to build what they're selling). They would have to add a margin for that uncertainty, which would price out some potential customers and limit how much they can make. Which (you guessed it) would result in those companies employing fewer people and paying less tax which pays for hospitals and schools.
Without investment bankers, pretty much everyone in the UK would be poorer. And would have fewer hospitals and schools.
It really doesn't matter that paying for hospitals and schools isn't their aim. By doing what makes money, they also increase productivity across the economy so that the government can pay for hospitals and schools out of the increased taxes.
Those hospitals and schools would have much less funding without the work done by the Finance industry. Both sets of roles are needed. The doctors and teachers and also the people who increase UK productivity so that the government can pay for them.