I'm not doing anything PROPORTIONAL to stake - you simply have to stake a given amount, somewhat like the master node scheme in DASH - but the amount shouldn't be very high - as there's nothing to WIN in staking, you don't care about your probability to mintmine, you only do it altruistically to keep the network running.
That is a flaw. Communism doesn't work.
There is a way to game your system because only those who are incentivized will mine (or those with more stake will dominate the mining). So for example, extortion and side-band fees. Or disrupting the system and shorting the token on the markets.
You were on the correct path of removing economies-of-scale from anything which can do harm such as double-spending. But as I said, there are other necessary details.