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Absolutely required may be a bit extreme. Its not absolutely required. A tilt-shift lens can offer you compositions you may be able to get with a standard wide angle lens, but it is certainly not a requirement. I shoot with my Nikkor 12-24/4 almost exclusively for interior architecture shots and it does fine. It needs distortion correction in post, but you will get distortion with any lens.
"Absolutely required" is more than a bit extreme, it is just false, unless you're shooting very tall buildings in a tight urban environment. I've been shooting commercial and residential real estate professionally for over 5 years now and have come across the need for a tilt shift lens only one time. The basis of this misconception of "absolutely required" is poor camera position. When many shoot interiors, they have the camera too high, causing them to have to "shoot down" into a room, causing converging lines. Conversely, when shooting exteriors many get too close to the structure and have to shoot up at it, once again resulting in converging lines. And this is where the tilt shift lens may be necessary: If you're shooting a very tall structure in a tight place, you may not be able to back up or get high enough (however if a neighboring building is in your way just shoot from that building ).
And also remember in this scenario: When we view a tall structure with the naked eye, guess what we see? Converging lines. You can leave a little convergence for very tall structures, especially viewed up close. This is how we naturally see them. For interiors they are pretty much a no-no, but once again they can look natural for very tall, close structures as this is how we see them naturally.