why would they care, if they pay a percentage of the profit made, why would they care if I trade everyday or not, so long as I make a reasonable amount each month and don't get paid a fixed income it shouldn't really make a difference
For the sake of this argument, let's assume the payout to you is 80%. Trader X is a part-time trader. Generates $100,000 in profits. The payout to Trader X is $80,000. Trader Z is a full-time trader. Generates $300,000 in profits. The payout to Trader Z is $240,000. Which trader is a prop firm going to accept?
Beggars can't be choosers? Prop capital for leveraged trading is allocated to each prop trader for the purpose of creating profits. The part-time Trader, when he's flying on a plane, is not leveraging prop capital, thus not creating profits, and thus wasting the allocation of prop capital. Prop companies want to allocated their capital effeciently and effectively.
If I was a prop group manager, my first impression, after reading this, is that your trading is not profitable. As a prop group manager, I would think that 10k deposit would be the least of your concerns if you're a profitable trader. You may be a profitable trader but the "first impression" I would get from this expectation is much different. I would think that a 10k deposit requirement increases the quality of the applicates.
BP isn't distributed in the way you think it is. They can take a risk that not more than X will be used at once, even if they give out 2 or 3x to all the traders, and if more than X is used, they pay some interest on a temporary margin call.