In Rogue Legacy, there is a limited form of freedom of choice, which I think is fitting.
Hmm... I think that the disconnect here may be in part that I'm not much of a player of roguelikes (although I'll admit that arka's idea here does interest me). I honestly think, however, that my response to being a "bad draw" would be to simply pick one, kill him off, then get another draw: I really don't like being told "no, you can't have that because the dice say so".
Additionally, I think that I recall watching Let's Plays of Rogue Legacy and seeing cases in which the player was disappointed in the selection available and didn't seem all that invested in that generation's character, moving quickly on to the next generation.
(While not quite the same thing, I have encountered something similar in playing an early version of Bro Force, as I recall: in that game, the player's next character was similarly randomly chosen--and I didn't like it. Again, I wanted to choose which character to play as, since I preferred some over others.)
I think that I'd prefer (relatively) complete control; rather than finding it boring, I think that I'd find a system like that in Rogue Legacy frustrating. However, I may well be in the minority on this, and may not be in the target audience for this game, so perhaps take my opinion with a grain of salt.
Of course, there's always the middle ground option: make it a setting. Allow users to select between three options: hardcore rogue-like, in which the next character is entirely random; Rogue-legacy's mechanism, in which the player selects from a randomly-generated set; and what I proposed above, allowing the player free choice.