...So going with the whole overtaking BTC idea, a masternode would cost $1,000,000, and the person would get paid out a 45% interest rate on block rewards. That doesn't sound very sustainable...
At the moment interest rate is ~9%, so I doubt it will be 45% then 
edit: "45% interest rate
on block rewards" - that's correct
Is there any reason why masternodes require a certain amount of coins up front to operate? Like a legitimate technical reason dictating requiring $20,000?
You mean 1000 dash, because not so long ago you could have it for $4-$7 each.
1000 it's a collateral, so you won't be able to operate thousands of masternodes for free and be able sybil attack the network.
If the price rises to btc parity, then masternodes and miners could vote for a decrease the amount needed.