When Sterling left QPR everyone accepted that he was trying to better his career. At that time, he had a better chance of 1st team football at QPR and he owed them far more loyalty than he now owes LFC.
Liverpool did well out of him, they got a quality player for a small amount of money, he's performed very well for them and they are now effectively making several hundred % profit on his sale.
He's off to better his career again, it's a step up to the Champions League and competing for the league. Yeah he risks spending more time on the bench, but he's backing himself again.
Presumably LFC will now use this money to prise other 'disloyal' players away from Southampton or Villa. Nobody will mention this of course, the narrative will be, 'good move for all parties'.
The real story here is that LFC had a guaranteed seat at the top table until recently. They are now learning what the rest of the league have had to swallow for years, that outside of that top four is a separate division. The four clubs that are there now may slip out of it occasionally but unless you can keep one of them out for 4-5 seasons in a row you simply cannot bridge the gap.