Many do though, the issue usually isn’t space, it’s how much money and who is going to pay for it.
London has some really good cycle lanes now with dedicated lanes, traffic lights etc. but it cost hundreds of millions to install and they only cover a tiny proportion of the roads.
To install it some roads will just needed to be demolished and started again and the whole road system on some parts needed to be completely re-designed and then there was a year of chaos while they did the work.
The other huge issue is NIMBYism, everyone wants more infrastructure but as soon as you mention narrowing lanes, removing parking or even removing lanes on a road someone uses regularly, they switch stance very quickly on the topic.
When they were putting in that Dutch roundabout in Cambridge, the residents were extremely negative about it, even as far as moaning about the colour of the tarmac and they have some of the best uptake of bikes in the country outside of London.