If someone compromises your StackExchange account can't they just unlink all your recovery options? Assuming they can't, the model is that:
- Losing any of the accounts linked to SE is a "compromise".
- If any of the other accounts linked to SE is not lost then you can "recover".
On this model, 2 seems reasonable by your own analysis:
- 0 is no good, you can't log in to SE at all ;-)
- 1 is no good, you have no chance of recovery following a compromise.
- 2 is the least number of accounts with non-zero chance of recovery. Provided that losing one does not compromise the other, then in fact it gives you a pretty good chance of recovery, since losing accounts is rare and losing two in quick succession is very rare.
- Additional accounts increase the chance of compromise, and the additional chance of recovery must diminish rapidly because the recovery chance is already good.
As I said, however, I'm not confident of the model. I've never tried to unlink something from my SE account.
The provided is quite a big one. If your Gmail account is also the recovery option for your Facebook, then losing your Gmail account means you've a fair chance of losing Facebook too. So adding Facebook to StackExchange would have a less dramatic effect on your chance of recovery following compromise via Gmail.