The first problem is that, because you don’t work for or have worked with Rangers, you will never really get a full picture of their brand. Designing without any business constraints is unrealistic in our industry. Example the word Ready in the logo is the clubs moto dating back to 1959, you're suggesting it be removed.
The second problem is that none of this will ever get implemented. Your case study will look shiny as a portfolio piece, but no hiring manager will care about it, no client will see it as real world work, but you might miss the opportunity to make a real impact in the world.
If you're willing to spend the time redesigning something that doesn't need doing, why not volunteer your skills to a cause that could really benefit from them? a charity, a local struggling business just to name a few examples.
I will take on board your note about volunteer work. However, the other comments are a bit much, it's only a concept. I am a life long fan of the club. The logo has not been updated in some time and I thought it would be interesting to create something. Whether or not it fits the clubs "business constraints" is not an issue, again, it's just a concept, for me, not for a "hiring manager" or anyone else.
Is designing for fun no longer allowed?
Our industry is increasingly plagued by people taking things (and themselves) far too seriously.
I think the best way to learn things is to do things, designing for fun is definitely one way that often i used to do to improve my skills.
No ones saying it not allowed. Just that perhaps there are better ways to spend the time. Whether someone wants to take that advice is up to them.
Everyone has probably done something similar in their career. I used to try and copy Carson, Sagmeister and Vignelli. The quality never got close, but it did help learn the tools. However in hind sight, whether it was an ideal way to do so, I'm not so sure.
Even though I'm personally not a fan of unsolicited redesigns, everyone is free to do them. Or not. It's their choice. But it's worth knowing there are other worthwhile alternatives.
And for what it's worth, I'd also argue that our industry is plagued by people who don't take it seriously enough.