The OP raises an interesting proposition. It's interesting for more than one reason. Not least, the timing of it. I don't think we would have seen this proposition raised after the Sheffield derby game, or the win at Leeds, but Brooks has had lean pickings of late and hasn't played with the same flourish as back in those games, so all of a sudden, the prospect of selling him and getting an injection of cash looks more appealing to some.
Another reason it is interesting is because it hinges on a huge assumption - that the sale of Brooks would significantly increase the cash available to spend on new players. It ought to, but this is a complicated calculation in itself, because if we look back at the sale of Naughton, Walker, Maguire, they were all sold for significantly more money than we saw pumped back into the club in terms of money spent on players. I think what's more likely is that we would see a small percentage of any sale of Brooks, put towards funds for new players, the majority of it would be swallowed up to support the running of the club.
And the other reason I find it interesting is that, to me, it shows a remarkable inability to recognise outstanding talent. Once in a while, maybe once every 30 or 40 years, a player comes along who has outstanding natural ability. I've been watching for nearly 50 years and in all that time I think I've only seen one for United - Tony Currie. Beyond Sheffield United I'd cite players like Alan Hudson, George Best, Maradonna, Eric Cantona, Paul Gascoigne. Got the picture? I'm talking EXCEPTIONALLY gifted, beyond the bounds of "normal". These players have one thing in common, apart from being extremely talented at football. They don't fit the mould. i.e. you can't compare them to other players in any way, shape or form. They are non-conformists. Let's take the great TC as an example and for those old enough to remember, I'll make some comparisons with others from that era (and if you're not old enough to remember - ask someone who is)...
Let's imagine John Harris back in the day saying..."X player is injured - let's get TC to fill in for him there". It couldn't have happened. TC in no way could have replaced Hockey, Salmons, Eddy, Dearden, Reece, Woodward, not any of them. He couldn't have, not because he wasn't good enough, but because he was just something else. He was a complete one-off. A special talent that could not be labelled, "a winger" or "a central attacking midfielder" or "a central defensive midfielder" or any other position for that matter. The same can be said of Brooks. Don't get me wrong, I'm not saying he's going to be the next TC - no one knows that. I'm saying he's a talent of that kind, that's my point.
The OP draws comparisons with other midfield players at the club and starts to suggest that Brooks isn't really a Coutts, or a Fleck or a Duffy and concludes from this that his value to the club would be best realised by selling him. I agree that he isn't like any other player at the club - and I think this is his real value to the club.
When you have a player like that in your squad you have to accept that they are "different" and that's what makes them special - the moment you start thinking about them as "an alternative to..." then you've lost sight of the jewel you have in your hand.
Would I sell him in January. No. Not a chance. I'd nurture the lad along for the next two or three seasons at least and let him be David Brooks - the talented enigmatic young man that he is. And watch his value soar through the roof. And when that day comes when we do eventually sell him, for several times more than he'd fetch in January, it will be like the sale of TC all over again. Because some players are just irreplaceable.