First of all, minimum fee doesn't require a fork. It's a network-enforced rule, and if some % of nodes would relax the fee requirements, you'd have a chance of having a lower fee transmitted to some miner who could include the TX in some block. Of course, firstly you'd have to tweak the wallet to create a TX with a lower fee than what's hard-coded into the wallet.
The fees are now dynamic, as explained here. The lowest possible setting is the minimum fee, and other, higher-priority settings are a multiplier of that. To sum it up, available fee multipliers are:
x1 (minimum fee, low priority), x4 (default), x20 and x166
There's a small set of possible fees to maintain privacy. If I used a custom fee, you could compile a list of TX-es which use some special fee and assume they are likely to belong to one single entity.
In words, the minimum fee could be defined as:
Fee such that, given a pool of TX-es offering minimum fee, the best strategy for the miner would be to mine a block at 100.6% of the current blocksize median, ie an 0.6% increase (actually anything between 0% and 1.2% would be economic, and 0.6% is just the "sweet spot").
In a mixed pool, it is always the smallest fee TX to get in a block which determines the optimum %. If there's enough higher fee TX-es, they'd kick out the small ones until the blocksize catches up with increased demand and makes room for those.
The x4 multiplier then means a 2.4% increase which is just enough to economically squeeze 1 typical TX above the min. blocksize, x20 one a 12% increase, and the extreme x166 one a 100% increase.
This means that the fee will go down with both time (due to reducing block emission) and increased usage (due to increasing blocksize). If the price grows linearly with usage (blocksize), the fees will remain constant in terms of fiat price.
There was a hiccup with this system when the TX size was increased with RCT HF, but nothing was done with the blocksize so TX-es became too big relative to min. blocksize and caused a congestion. This happened because adding just 1 TX over the median would have meant a 23% blocksize increase, requiring huge fees to be economic for the miner. Because of this, the min. blocksize was increased in the April 2017 HF.
With the current ratio of typical TX size and min. blocksize we should be fine "forever". The upcoming range proof size reduction will only help this as it will drive the ratio further down. Once the network organically "permanently" pushes the median blocksize above the min. blocksize, it will only get better and better and the dynamic fee/blocksize combo would be working more and more smoothly.