I don’t think the reason they give out coins is to help free players compete. They could easily give out some OP league store toons or release legacy ascendables to balance the competion between f2p and p2w
I think the reason they give out coins when it may seem free is similar to a store giving out a free sample. They want people to have a taste and then buy the product.
Also I believe they give out free coins with the intention of getting players to spend more time on the game (leagues, old daily mission coins) thus furthing the bond between the player and their product.
The more time you have invested into something the harder it is to leave it all behind