Uh, the way I understand what you say: the bitcoin price, is the price of 1 BTC in $$, right ? Commensurate, is proportional, right ?
Let us say that the proportionality is 0.0001. Then that means that a fee is 0.0001 BTC, no ? So if BTC = $1000,-, a fee is $0.10, if BTC is $1000 000,- then the fee, with the same proportionality, is $100,- , no ?
Or do you mean "transaction amount" instead of "bitcoin price" ?
But then the miners will only take those transactions with highest absolute fee, so only the very large transactions. Because for them, at a certain point, including an extra transaction (and risking the loss of the entire block) will not be beneficial any more below a certain absolute fee.
This is why I only consider seriously anonymous coins, like monero, and to a lesser extend, zcash (lesser, because not compulsory anonymous). (DASH is a joke in that respect).
But people will soon learn this, and it will be another reason to avoid bitcoin.
It is very unwise to avoid bitcoin. Besides, bitcoin never promises anonymity. Instead, it promises (a certain level of) privacy. Whether a cryptocurrency is fully private or otherwise, requires the recognition and support of the shadow government to work. Or else it won't. If I were to issue a better version of bitcoin into the world, nobody would give a shit about it and it would die out within a year. Where will I get the money and the resources to promote it, to have a bunch of guys traveling around the world convincing everyone about how good is my version of bitcoin, to convince the exchanges to list my version of bitcoin, to convince companies like Microsoft, Overstock, Ernst & Young to accept it as payment, to convince governments to legalize it, etc etc etc? It may be a better version but unless it has the kind of support backing it, the same kind of support relentlessly backing bitcoin since 2009/2010, and expanding, it will never survive no matter how good it is, no matter how private it is, no matter how secure it is.
Bitcoin was a unique possibility for a few initial players to become immensely rich ; and they had the right timing: after a financial crisis, it was easy to get a big crowd of enthusiastic believers on their hands. These financed the initial gains of a few whales, who then, had enough means to promote it more. Such an opportunity happens only once. There is no need for "dark forces" behind it: in fact, the failure of bitcoin to get seriously adopted indicates rather the fact that there are NOT very powerful dark forces behind it. Bitcoin was just a hype with right timing, some distrust in banking, and unrealistic promises (that can't be accomplished with its technology, but which need sufficient technological insight and lack of starry eyes), sufficiently enthusiastic useful idiots and so on. Overstock was a family affair: the big boss of overstock was talked into bitcoin by his own son. Microsoft was on the look to hook onto any hype that could pull it out of its morass.
If there were powerful dark forces behind bitcoin, they would have twisted Amazon's hand to accept bitcoin: the story would have been entirely different. Bitcoin, as a payment system, is essentially a failure. However, as a greater-fool game, it works marvellously, for the time being, like all greater-fool games, that promise quick riches (and yes, there are a few hundred of quick riches in bitcoin, living off all the donations by the "adoption" crowd).
You are underestimating the explosive combination of useful idiots believing in some libertarian dream, combined with the power of greed and the illusions of quick rich. THAT is the power behind bitcoin. Not "organized dark forces", but an explosive mix of foolish idealism and greed. It is what keeps it up, and this is more powerful than any cigar-smoking "elite" making evil plans that never work out as expected. Greed and naive idealism. What more do you need ? What is better than naive people thinking that their idealistic nonsense is going to make them immensely rich, combined with some smart money that sees the opportunity to exploit this enthusiastic propaganda for making a lot of bucks from starry-eyed greedy idealists "adopting" their new toy ?