They are not. Choice among several query plans depends on various summary statistics about the data, which might not be the most recent.

Including the input parameters.

It's not unusual for us to end up with bad query plans because the shape of our data can vary pretty greatly. In many cases, a Foo has 1 Bar. But in some cases, a Foo has a million Bars. That can cause the query optimizer to treat lookups on the bar table as if there are few elements there (causing a scan instead of a seek).

For the general case, the optimizer gets it right. However, the fringe case is one that causes the entire system to crash. It's a bit akin to how an insertion sort can be faster than quick sort when n is small. The optimizer might make a bad assumption about the size of n which makes it pick an expensive n lookup when log(n) is available (but slower for small n).