Children today are growing up seeing games as services that are always and anywhere available. Adoption among young players should be good, especially since the parents don't have to buy an expensive plastic box. I believe the success is all up to 3rd party support. The convenience and quality for streamed gaming will only grow and if 3rd parties jump on it it's only gonna be a matter of time until it develops into a successful industry.
If the parents have to pay 20-30 dollars/euros a month for their kid to play, and hear them scream anytime there is some lag, they won't keep the subscription for long and will most likely buy a Switch, lend their phone with F2P games, or buy a cheap tablet / old console.