What you’re seeing is a mix of perspective and lens distortion, plus the fact that a strong correction can look unnatural because we’re used to seeing tall buildings “lean” when viewed from ground level.

For the most natural result:

• Keep the camera level if possible. Tilting the camera upward causes converging verticals.
• Use a wider lens and place the building higher in the frame, then crop.
• Best of all, use a tilt-shift/shift lens, which lets you keep the camera level while fitting the building in.
• Shooting from a higher viewpoint can also help.

In post-processing:

• Apply lens distortion correction as well as perspective correction.
• If your software uses automatic lens-profile correction, do it before cropping, or switch to manual correction if cropping confuses the profile.
• Decide what you want straight: with a single 2D transform, you often can’t make every plane of a 3D building look perfect at once.

So yes, post can improve it, but there isn’t always one fully “correct” result. Often the best image is a moderate correction that keeps the building believable rather than forcing every line perfectly vertical.