Okay, let's do some math. Very rough napkin numbers, but it'll get us close.
A 150Hz blink rate means a period of 1/150s, or ~6.7ms.
The speed of radio signals through air near the surface is a bit lower than c, let's call it 299,250 km/s. [0]
When you multiply those numbers you get ~1500km. That means each 'on' and 'off' signal is 1500km long, moving near c. More specifically, the signals are concentric rings around the transmitter 1500km in width.
Let's look at London. I picked it at random, but it just happens to have a land area around 1500km^2. Assume the transmitter is in the center of the perfectly circular city, that means it takes 3.3ms for each 'on' and 'off' signal to cover the entire city. Each on and off pulse is just about exactly long enough to cover the entire city.
All that together means that at any given moment 50% of the lights in the city are on, and the other 50% are off. That's about as far from synchronized as you can get, really.
Also, light is slightly faster than radio in these conditions[1]. The light reaching the center of the city won't be pulsing in the same phase as the signal you're sending out. It will also be blurred and muddied due to the difference in signal speed. You probably wouldn't see much flicker in the light at all, as 50% of the lights are always on. On average, you receive 50% of the light you would otherwise, but that value will never reach 0. There won't be any periods of total darkness where you can make an observation, as the article suggests.
Moral of the story: light (and radio) is much, much slower than most people realize.
[0] https://ieeexplore.ieee.org/document/170108
[1] I couldn't find a confident number in my 16 seconds of searching. Seems like just a few percent faster, but the real number doesn't matter here.
Bonus: you can synchronize the streetlights exactly, but it's much more expensive and complex than a single radio transmitter. You need to have every single light contain a receiver with an accurate clock that synchronizes with a geosynchronous satellite with an atomic reference clock. Search for "GPS disciplined oscillator" if you're curious.