Everything is full of humans, but private companies with terrible processes workers would usually have consequences that demand some change. Government services have no competition sos they are exempt from consequences if they're terrible.
There is no perfect competition, supply doesn't perfectly meet demand, and incentives aren't always perfectly aligned ¯\_(ツ)_/¯
In any case, government services change through policy and, thus, indirectly, through the electorate. But a) it lags, b) is not the only issue the electorate care about, c) the supply of money is not infinite, d) the supply of labour is not fungible and e) in this specific case, policy on immigration is generally driven by people not immigrating, so the incentives are not aligned.
Meanwhile I can't choose between other government services while in Germany but those terrible forced upon me by the state.