This is false. A fixed route is predictable. You know when it will be there and can plan for it. Non fixed routes mean you cannot be sure when your ride will arrive and thus cannot be sure you will arrive on time.
That makes the fixed route better than a flexible route. Sure the flexible route is faster in the best case. However it is unpredictable and people have deadlines of when they can arrive: a flexible route cannot meet those consistently enough.
Bus routes can be fixed in the sense that they can stay in place for decades. Even simple things like paint, signs, and shelters provide psychological permanence.
Things like WalkScore show up on real estate listings as a value add.
You don't even need that. Just seeing the bus go by "all the time" provides permanence. Really it is better, I've seen plenty of paint/signs/shelters, but when I bothered to look the bus only came rarely. When I moved someplace where I saw buses all the time I realized I could use them even though there was no paint/sign/shelter close to where I got on.
That makes the fixed route better than a flexible route. Sure the flexible route is faster in the best case. However it is unpredictable and people have deadlines of when they can arrive: a flexible route cannot meet those consistently enough.