I don't quite understand your argument.

Assuming there is (1) a distinct linear trend between block reward halvings and (2) these linear trends continue to get steeper after each halving, then the long-term trend will be exponential, not linear.

You could chop any exponential bubble chart into small pieces and draw a straight line through each of them. The complete chart will still be exponential. When talking of a long-term trend you should draw your trend lines on a single long-term chart. Then you'll notice that it doesn't look linear at all.