There are already various forks of bitcoin which do this if this is what you are looking for, although be prepared for your money to be worthless since they all constantly devalue against bitcoin since nobody actually uses them.
Well to be fair, bitcoin itself isn't tied to anything of value. So it really has no value other than perceived value - the value people attribute to it in their own head. That is one of its weaknesses. Creating bitcoin and then trying to layer value on top of it by hooking it up with stablecoins is not an ideal solution. As we can see, stablecoins have their own issues. One of them being they are not trustless. So the value bitcoin has can't be considered trustless if bitcoin is ever based on one.
Yes of course the value goes down since nobody needs the 5th fork of bitcoin that has nothing else than a little bigger block size, but thats not the point. If you for example don't like the Bitcoin logo you could also create a fork with a better logo and nobody would use it. Still it would not mean that people are not satisfied with your new logo.
That's a minor issue with bitcoin is that someone can make a duplicate copy of it and the only difference between their copy and the real bitcoin is the popularity of one of them.