I guess the worry here is that it's possible that bitcoins could end up being worth a lot more than they are today. For example, if 0.01 BTC works out to be the equivalent of $1 today, then that built-in 0.01 transaction fee is far too high.
If there is some way to make the transaction fee scale with the worth of the currency that would be best, but I can't think even conceptually how that could be possible. It's not like the currency has any idea how much it is worth in real terms.
Ideally, you raise the ceiling in this situation. Right now, there is a 21 million coin limit. So as the value goes up, so does the ceiling so to speak. Unless one person has 20 million bitcoins and the rest of the world has to trade with 1 million, there should be no reason go in the opposite direction for the value to value comparison. But I do understand exactly what you mean though because some world currency is traded like that where 1 unit of XYZ country equals 20,000 of another, so small decimal values have to be used.
Since the transaction fee can't get below 0.01, the value should always be greater than the fee, otherwise, people are not making any financial sense. It would be like living in a city where it cost $10.00 to drink from a water fountain. The business model should fail in light of free, public water fountains outside, so who would bother to pay that much money when the alternative makes more financial sense.
Same way with the 0.01 fee limit, people already expect it and won't value things beneath it as it wouldn't make financial sense. If the lowest possible fee is 0.01, why would anyone sell anything for less than that? You would put yourself out of business quickly.