Would it have been a better longterm strategy to incorporate the client kingdoms into the Empire as provinces instead of having to pay them bribes indefinitely?
Not really. The way the Romans went about their frontier politics was ingenious. Paying small tributes that really didn't have much impact on their finances to keep client kings from being overthrown and playing tribes against each other. Really, it wasn't until the Huns that standard Roman frontier politicking wasn't going to cut it any more.