5000 lottery prizes twice from 60 spins, but no 500 or 5000 satoshis and RPs prizes. If the probability of hiting bigger prizes is the same, despite them being satoshis, lottery tickets or RPs, why do lottery tickets visibly happen more frequently? Is the answer simply luck or the lack of it?

They are not the same.
The chance of winning each of 5000 satoshi and 5000 Reward points prizes is half of the chance of winning 5000 lottery tickets.
For winning 5000 satoshi, you need a number between 998,999,959 and 999,999,958. So the chance of winning 5000 satoshi is 0.1%.
For winning 5000 reward points, you need a number between 331,308,320 and 332,308,319. So the chance of winning 5000 reward points is 0.1%.
For winning 5000 lottery tickets, you need a number between 664,616,640 and 666,616,639. So the chance of winning 5000 lottery tickets is 0.2%.