I don't think they are "effectively unlimited" either, perhaps closer to "effectively dividable forever", which might not be true, not sure. However, once they are in full circulation they will be a deflationary currency, and giving someone a sliver of a bitcoin that's worth as much as what a full bitcoin was worth at X time in the past is not the same as adding more bitcoins.

I remember one of my economics professors always pre-pending "All other things being equal" before, relating any theories. I keep that in mind every time I start thinking about anything to do with economics, the pile of assumptions on how things are going to work is usually problematic.