The original paper says only:
Once a predetermined number of coins have entered circulation, the incentive can transition entirely to transaction fees and be completely inflation free
Why is it desirable to be inflation free? What are the downsides to this approach?
Paper money essentially is an IOU with a specific value at a specific time. If the value of the underlying currency changes after that point in time that changes the incentive to pay back that IOU because the amount owed is still the same but the underlying value of that amount is different.
The assumption with Bitcoin is that rather than a debt Bitcoin is an asset. If that asset becomes more valuable relative to the market you'd simply pay less Bitcoin for the same goods, simply because you don't have to worry about its value relative to a loan you've either taken out in the past or you're going to take out in the future.
That's the idea at least. Time will tell if it really works out that way but the theory seems to be sound.
Hyperinflation is bad of course, but moderate/controlled inflation is a need to make a currency works IMHO.