There was a recent discussion on the Pelgrane Press forums about whether or not Flexible Attacks are a desirable mechanic for 13th Age. The main concern is that the Fighter, the ultimate warrior archetype, "doesn't get to choose how to attack" (HomegrownHydra on Dec 1st). Or, put another way, "it's hard to feel narratively empowered when a random dice roll determines the very thing you attempted to do rather than its mere success or failure" (lessthanpleased on Nov 25th).
Here's my take on the issue. Sometimes all it takes for a mechanic to be viewed favorably is for it to be explained well. I think the Player Sidebar under Flexible Attacks does a poor job of this, implying that flexible attacks are limiting: "you can be certain the attack you're describing plays out the way you're telling it because you'll already know if you hit or missed." I can easily see this leading to the perception that flexible attacks mean "roll to determine what you can attempt." And yes, saying "you can't do that" runs counter to the design philosophy of 13th Age. Rather than saying your options (in the fictional game world) are restricted by your die roll (a model in the real world), consider the following example.
A Ranger (with the Double Melee or Double Ranged Attack talents) defaults to attempting a double attack with their action. It's not that they're not swinging both weapons when they roll odd, but rather the second attack simply didn't hit, or the opponent never presented an opening, etc. The die rolls for the player are not contradicting the fiction of the multi-attacking Ranger. Or at least I haven't heard of any player complaints to the contrary.
Think of a Fighter's flexible attacks in the same way, but with an added twist. The attack roll resolves TWO actions, the first being the attack (determined by comparing the die roll with the target's AC) and the second being the intended secondary effect that the Fighter is attempting (based on the natural result of the d20). Say that a Fighter says "I'm going to Shield Bash this fool" but rolls a 17. Odd number indicates that the shield bash part of the attack failed (analogous to an attack that simply rolls too low to hit AC). But wait, the Fighter is SO GOOD at fighting that at the last minute he can decide to do something ELSE with his action. "Roll of natural 16+, I'll use Precision Attack instead!" One way to narrate it would be that the shield bash, while not strong enough to pop the opponent off of you, did cause it to momentarily lower its defenses allowing for a quick jab. Point being, just because you don't HAVE to telegraph intent by choosing a flexible attack beforehand (unlike, say, the Rogue, who does choose a specific power) doesn't mean that you HAVE to wait until after the die roll to decide the fiction.
In short, rather than saying that your Fighter just attempts whatever the flow of battle allows him to react to, think of the Fighter as failing in his initial attempt but getting a second chance at doing something else (assuming he triggers a different maneuver). Or, alternatively, you can simply say that your Fighter will rush in and then attempt whatever he sees an opening for. Different perspectives on the same mechanic, neither of which limit the fiction of what your character attempts.