Is your objection that the monetary base would grow without bound?
It would need to, or we'd rapidly hit that bound, and then new users would come in and post threads like this one, whining about the early adopters having all the coins.
In other words, even an S-Curve model like Kárhozat proposed would still have the tail of the S, which you argue will be indistinguishable from Bitcoin's logarithmic curve once you get past the bend.
Decent argument, unless the bend is placed such that the currency must be assumed to be either widely known (so that you can credibly state that people "had their chance") or dead.
(Like I said earlier, the placement of the bend is
the trick here.)