On underground lines, the PSDs are mostly for air-sealing. It allows you to air-condition the platforms without trying to cool the tunnels, and it helps the piston effect of moving trains pull air through the tunnels, rather than just swirl air around each platform.

Also probably helps for fire engineering.

The Elizabeth line is already built with platform screen doors, although I believe they’re only on underground sections. I don’t know enough about this station to say whether it had them; I expect not.

Platform screen doors tend to be used underground mainly for airflow management. They are not primarily for safety.

They don’t work well outside. No overhead structure to anchor to, weather has a larger impact, and they can become something to climb rather than an obstacle.