You are right in the longer term but surely wrong in the shorter term since history records The Byzantines paying off Attila the Hun from the 430s to the mid 440s, so a 10 year window.
The Danegeld lasted over 150 years. It undoubtedly failed in the end, but it certainly worked in the short to medium term.
The Sassanid and Byzantines paid off each other for ages. The persians paid tribute for a long time to border states.
The pre-french kings paid off The tribes who eventually became the Normans.
It's a shit long term strategy. Doesn't mean it didn't work in the short term for the states using it.
Remember, these tributes were clearly liquid cash, or equivalent. When they ran out of money it seems to turn into land. The implication they could NOT have been used to raise forces internally begs questions. The counter argument I suggest is that you raise an army (that you don't have to pay) when you CANNOT pay off the other side, or don't want to cede land.
Perhaps where we meet is that history records states doing it but it didn't work in the medium-to-long term. Did it happen? Yes. Did it work? "no" for a long term view but the immediate effect, for some period of time? Depends how you view it.
The same might be said for the condottieri. Groups like the English "white company" in the extended wars of europe in the middle ages. Paying them to switch sides might be more effective than putting up your own guys to fight them.
[Edit: I invite people to think about the average lifespan in role of ancient leaders, and what a decade or a hundred years means for "success" or "failure" against those measures. Bear in mind that most modern democratic states operate on a change of leadership in a 4 to 6 year timescale, with some cycling much faster and some cycling much slower, and it is rare for a successor leader to entirely endorse his predecessors choices. Now cast that into pre democratic times and ask yourself what success looks like.]