I wish there were a pool which rewarded the block finder with 12.5 BTC (the remaining 12.5+fees would de divided between all miners, just as a normal pool).

The total network hash rate is 120.000 TH, so even with just 1TH you play a game with reasonable odds.  Within the next 10,000 blocks (~2 months) you have an 8% chance of winning.

This would also help the network. Individuals would play for the same reason they participate in state lotteries. They are likely to "over-invest" (which they btw do all ready) so that the expected return turns negative. Large investors with data centers would be forced out.