The fees are already linked to fiat in a way.
Lets remove that ambiguity and make it clear? Don't you agree with that? 
It not ambiguous it is the market forces of supply and demand, they affect Bitcoin in the same way as they do fiat currencies. The important part of your suggestion was to remove that and have fixed fees. I don't think that is desirable.
Well this is the point where bitcoin becomes a tool for the elites and less of a payment system for the masses.
You could argue that but I would say that's why some altcoins are doing so well. We're all free to chose whether or not we use Bitcoin for transactions. Long term I see fees reducing drastically when Lightning Network comes in.
Not sure about this part. Miners may decline to accept all the payments, what will happen then? They may argue that they want atleast 30Sat/byte etcs.. Have to think about this part..
Miners really are not a single entity. If some miners choose not to mine transactions below a certain fee then others will when they are the only transactions left with a fee on them. If you keep a close eye on what is in the mempool you'll see that it usually clears out completely after a period of congestion like we have had recently, even transactions of less than 1 sat/byte get confirmed when there is nothing else left.
