Why does OP have to clear immigration at TXL (unless the airport physically doesn't have an airside for non-Schengen to non-Schengen transfers)?

OP does have to clear security not because the outgoing flight is heading to US but because the incoming flight was non-EU.

If OP ends up TXL-JFK-MIA, the stroller will come out at JFK due to US requiring every passenger to clear immigration and customs at first US port.