My London borough (Haringey) does not do this and only use the Source network for which my home is equidistant to several... being more than 1km from all of them. No letters or pleas, or offers from myself to fund installation of lamp post charges in line with govt grants have been successful.
I'm going to be purchasing another fossil fuel vehicle as it's clear that electric won't work for me unless I can get the distance to a charger below 100m.
Oh... and charging from the property by running a cable over or across a path is apparently against the law: "Highways Act 1980, it is illegal for any person to place or run a cable or wire along or across any part of a public highway. So running a charging cable across a footway is not permitted" (excerpt from council reply to my enquiries).
The underground cables for streetlights have been dimensioned for the power draw of light bulbs (~100W each), not for a charging car (10kW or more).
Even if you change those cables: The distribution box for those streetlights is only dimensionded for say 100 lights (~10kW), not 100 charging cars (~1MW).
Even if you change the distribution box, the cable to that distribution box... well you get the point by now.
So, the increase in power need (according to your 1 kW) is between 4 and 10 times.
Also if a lamp post is every 30 meters and each car takes 5 meters, each post needs to serve 6 cars.
And we are already between 24 and 40 times.
Besides, how long is the cable of an electric car (the one on-board)?
You will need to have a 20 m cable on board if you happen to park in a spot mid-way betwen two 30 m spaced lamp posts.
Who will finance the new installations?
Where will the newly added (or enlarged) electric cabins be put (in already densely populated/built EU cities)?
Similarly loading infra won't be able to to handle everybody suddenly needing their cars fully charged from empty. For the rare cases where people actually need more range than can be filled over a day with low power charging, there can always be a separate network of fast chargers. There is absolutely no need to design every parking spot for fast charging.