Because calculating luck requires computing power, computing luck is also expensive, a single node cannot try many luck values.
Saying that it "requires computing power" is the same as saying that calculating difficulty "requires computing power". Pools can just create some math formula like "totalEffort=constA*luckValue+constB*difficultyValue". Maybe for luck this "constA" will be higher than "constB" for difficulty, and also difficulty depends on luck, but after all everything comes to overall effort of mining a block that can be somehow calculated. And mined block that does not meet network difficulty, but meets 10 or 100 times easier difficulty is called "share".
To mine such "shares" there is no need to stop typical, honest mining. These shares could be merge-mined and sent somehow between pool nodes. And even if mining reward cannot be distributed from coinbase, it could as well be shared in a normal transaction. There is nothing that can stop miners from mining both luck and some "luck-based sidechain with lower difficulty" containing shares for some pool. And finally some of these shares will be below network target and will be treated as any normal block, paying everyone its reward.
In this way instead of one person getting one coin per day, it could be 100 people getting 0.01 coin (or maybe 0.0099 assuming pool fees around 1%) every ~15 minutes, if they have similar computing power. And even if there are more and less powerful miners, such rewards could be set accordingly to the number of shares. Because now luck is also based on "winner-takes-all" model instead of "everyone-gets-something-every-block" model, so there still will be some pressure to be "the winner" as often as possible. In other coins, pools are such winners when there are many miners and winning a block is more and more difficult and takes more and more time.
Of course, in a long time perspective it is more profitable to solo mine, because of mining pool fees, but such fees is nothing more than paying for getting something faster. And as there always will be some people in hurry, there always will be some need to pay someone for getting some coins faster than usual. And that is why some pools will be created sooner or later.