That's an interesting take. I'm reluctant to accept that Minamino is happy enough being a squaddie. Also, my impression is more along the lines of no club was willing to match our price for Origi and he's more than happy to stay. With Minamino it was more a matter of him grinding down this January window to prove himself here instead of another loan because he's already had one before. Wasn't Henderson also offered an exit years back earlier when he just joined for a few years but instead stayed on? Would be interesting if the club decides to extend the contracts of both Minamino and Origi whenever the time comes.
I think that that attitude is quite understandable in quite a few players. There are others that wouldn't be happy, or aren't after a certain amount of time when they start to get itchy feet (Phillips) but there are quite a few factors that can influence a player to remain as a squad player even knowing that's all they'll be - though the manager is a key factor I feel.
Let's take Taki for example :
He's now at one of the best clubs, and on the verges of one of the best teams, in the world. Where would he be otherwise?
He has a chance to play (be involved) in some of the world's best football matches (even if only sometimes coming on as a sub). He wouldn't get that elsewhere.
He's no doubt paid a very handsome salary that would be hard to match playing for a lesser club.
Playing for Liverpool, even as a squad player, raises his profile dramatically enabling other opportunities (sponsorship and post football career media).
In just 2 years at LFC he's now got a PL winner's medal (14 games) & a LC winner's medal. He definitely wouldn't have them elsewhere.
Of course this will vary player to player but Origi is another one who has an incredible record for a squad player.
Whether you'll be happy as a squad player will depend on the personality of the player. The more team minded you are (easy to understand with a Japanese player) the more likely you'll be happy in that role. The more individualistic, maybe less so. Neither is wrong they are just career choices.