Would you consider making edge costs visible when discussing with a guildmaster? I can't see why allowing players to see the cost of an edge would be bad, but it would make choosing them a bit less random (similar to thief points), as you could actually plan a bit and for example pick a couple of cheaper ones instead of probably just the one near the top of the list (of course there would still be some ambiguity, because you wouldn't know your exact edge point total, just that you have at least the amount for the most expensive one(s) on the list).

I.e. when discussing you would see something like this (with the edge point cost in parentheses after each edge):

You can choose the following edges:
Deep Pockets : You can develop deep pockets, capable of carrying more things. (4)
Combat Statistician : You can be a combat statistician and analyze battle more precisely. (4)
Courageous : You can show courage surpassing most. (4)
Apt Learner : You can become an apt learner, garnering more from your experiences. (4)
Lucky : You can be lucky. (4)
Mousy : You could explain to your guildmaster the reasons you are unmoved by epic song. (4)
Humorless : You can explain to your guildmaster the reasons you are unmoved by comic song. (4)
Stonehearted : You can tell your guildmaster about your disinterest in romance. (4)
Cheerful : You can tell your guildmaster about your cheerful nature. (4)
Dove of Spring Dawn : You can learn to meditate and heal faster when calm. (4)
Leader : You can be a natural leader. (3)
Stone Shoulders : You can learn to do slightly more damage with your bashes. (3)
Swath of Destruction: You can learn to leave more severe wounds when you slice your foes with a polearm. (3)
Prone Defense : You can learn to better defend yourself while prone. (3)
Strong Back : You can develop a strong back, more able to bear heavy loads. (2)
Battle Tested : You can learn to slumber more quickly after the excitement of combat. (2)
Transportation Sensitivity: You can hone your senses to detect transportation magic tugging at you. (1)
Cover Up : You can learn to better block attacks aimed at your face. (1)
Shield Eyes : You can modify your fighting style to better shield your precious eyes from harm. (1)