Sure, it's a trade-off, we probably just disagree about the level of risk involved and the benefits gained.
As you say with FB login there are ways to mitigate that risk, but to take one example - if FB charge for the service in future at 0.01c per use, many of your users will still want to login with FB because it's easier for them, and you'll be stuck with the bill. This happened with sites using google maps in 2012 when they started charging - each of these decisions has to be weighed up individually as a risk, but I think login is too important to delegate to another site and a significant addition of complexity and risk.
It's not one level of risk-reward, you need to take a look at your specific case to make the call. Formulating a blanket opinion about this outside of a specific context is not wise.
That said, your example doesn't demonstrate much risk at all. What are the incentives for FB to start charging for this? It just doesn't make any sense for them to give up that data and that control to try to squeeze existing site operators out of a buck. I mean, never say never, but the risk is much less than it was with Google Maps where you always had to be asking what Google was getting out of this expensive and difficult-to-build-your-own service.
As you say with FB login there are ways to mitigate that risk, but to take one example - if FB charge for the service in future at 0.01c per use, many of your users will still want to login with FB because it's easier for them, and you'll be stuck with the bill. This happened with sites using google maps in 2012 when they started charging - each of these decisions has to be weighed up individually as a risk, but I think login is too important to delegate to another site and a significant addition of complexity and risk.