Further, after significant involvement in the interview and hiring process at my last position (a very large technology company), it's my belief that this would be counter-productive to most firms. Finding candidates that have the skillsets necessary, fit the culture, and perform well in the interviews is difficult enough.
I didn't need transcripts though. You don't need a transcript to verify that someone obtained a degree.
Plus, while it does not matter whether you have degree for programming, it does matter whether you lie about it.
Your comment on "fit the culture" can be considered somewhat offensive, and an indicator to candidates that they may want to consider other opportunities.
I think you're a ways off here. Culture is character (and not a "bundle of soft skills"). Some companies want candidates that value and empathize with customers. Others may want candidates that demonstrate integrity and ability to collaborate with others. Often, these values are codified as principals to work and measure by. When a candidate fails to demonstrate valued traits, or provides examples that are contrary to those values, that is "not a culture fit".
Because "culture", in vernacular, does not mean what you propose. Would you agree that it broadly consists ofthe shared history and norms that bind a group together socially? That's not a bad thing in and of itself, but it does implicitly defining other people as outsiders. When you add "fit", it can become exclusionary. That's what I mean by the term legitimizing bias.