I mean, I think you genuinely believe that what you suggest is simple... so, I won't pretend to not understand how you might think that. I'll explain:
There's simplicity in performing and simplicity of understanding the process. It's simple to make more humans, it's very hard to understand how humans work. When you think about using pip with requirements.txt you are doing the simple to perform part, but you have no idea what stands behind that.
Unfortunately for you, what stands behind that is ugly and not at all simple. Well, you may say that sometimes it's necessary... but, in this case it's not. It's a product of multiple subsequent failures of people working on this system. Series of mistakes, misunderstandings, bad designs which set in motions processes that in retrospect became impossible to revert.
There aren't good ways to use Python, but even with what we have today, pip + requirements.txt is not anywhere near the best you can do, if you want simplicity. Do you want to know what's actually simple? Here:
Store links to Wheels of your dependencies in a file. You can even call it requirements.txt if you so want. Use curl or equivalent to download those wheels and extract them into what Python calls "platlib" (finding it is left as an exercise for the reader) removing everything in scripts and data catalogues. If you feel adventurous, you can put scripts into the same directory where Python binary is installed, but I wouldn't do that if I were you.
Years of being in infra roles taught me that this is the most reliable way to have nightly builds running quietly and avoiding various "infra failures" due to how poorly Python infra tools behave.