Good post, but there are some errors in it.

By the end of the year (not including the initial high issuance rate during the first year), the 10% not going to existing SP holders is distributed as follows:

• 1.5% goes to block producers (witnesses and miners) directly as SP.
• 0.75% goes to liquidity providers as STEEM (actually currently it doesn't because liquidity rewards have been temporarily disabled).
• Some amount between 2.906% and 3.875% goes to authors as SD (depends on how much users vote during the reverse auction period).
• And the remaining amount somewhere between 3.875% and 4.844% goes to authors and curators directly as SP.

Keep in mind, the above numbers are still an estimate which does not take into account more complicated effects that depend on user actions and market conditions that are hard to predict, such as the price changes of STEEM relative to USD, powering up/down, and conversion of SD to STEEM.

But with the above estimates, and an assumption of user behavior regarding voting during the reverse auction period, one could roughly estimate the distribution of that 10% to the various different asset classes as follows:

• 6% goes to new SP ^{(Thanks to @anonymint for finding my arithmetic error that caused me to incorrectly write 5.5% here originally.)}
• 0.75% goes to STEEM
• 3.25% goes to SD

Regarding your precise model, I'm having trouble making any sense of it. I've tried modeling it myself assuming that the system rewards authors with STEEM instead of SD (to ignore the complicated effects due to STEEM price changes and conversions) and assuming that the fraction p of the total STEEM supply held as Steem Power remains constant throughout the year (meaning users power up or down as necessary to maintain that fraction p). I also define d to be total annual issuance rate (i.e. d = 1 in the design of the current system since Steem is designed to issue 100% of the total STEEM supply each year as new STEEM) and v to be the fraction of all newly issued STEEM that goes towards the vest pool (i.e. v = 0.9 in the current code).

The result of that model is that the effective annual growth rate of one's fractional ownership of the total Steem Power (assuming they do not power up or down and do not earn any Steem Power rewards) is given by the formula:

Click here to see a plot of the annual growth rate (expressed as a percentage) of one's fractional ownership of total Steem Power (again assuming they do nothing with it), which is the vertical axis in the plot, versus the fraction of the total STEEM supply that is maintained as Steem Power throughout the year, which is the horizontal axis of the plot.

I think the alternative design you propose is interesting. If you include the compounding effect, the worse case annual loss in fractional ownership of total SP is still only 8.7% (which is only a little bit higher than the current worst case rate of 6.7%), while the dilution of liquid STEEM is, as you mentioned, reduced to a 16.7% loss per year.

We can explore other possible configurations under the same constraint that 10% of the overall STEEM supply is issued per year for the purpose of paying/rewarding users (block production, liquidity rewards, and content/curation rewards). See this plot (the first one on that page) to see annual percentage loss of fractional ownership of the asset, the vertical axis, for Steem Power (the bottom blue line) and STEEM (the top red line) in the scenario where those assets are just held for a year without earning any new rewards and 95% of the total STEEM supply is maintained in Steem Power throughout the year. They are plotted against annual STEEM issuance rate as a percent, the horizontal axis, which ranges from the minimum of 10% (which means all issued STEEM goes to rewarding users and none goes into the vest pool) to 100% (which is the annual rate the current Steem code is designed to issue new STEEM after this first year).