The 44 comes from a rounding gap, not a design choice.
Bitcoin Core's GetBlockSubsidy (src/validation.cpp) starts at 50 BTC in sats and does nSubsidy >>= halvings, so every halving drops the fractional sat. Add up all 33 reward eras x 210,000 blocks and you get 2,099,999,997,690,000 sats. That's 2,310,000 sats (0.0231 BTC) short of 21M. The subsidy reaches 0 at block 6,930,000 (around 2140).
Fill that 2,310,000-sat gap at 1 sat per block: 2,310,000 blocks / ~52,560 blocks a year (144 a day) = about 43.9 years. That's the 44.
So a 1-sat tail emission could run ~44 years before total supply passes 21M, but it would pay miners only 0.0231 BTC over that whole stretch. It's a joke about the security budget, not a fix for it.
