Sure, gut instinct is right at times. However, there are great problems with it.
Let's make the assumption that many a court makes: Officer Smith has been on the street for years and will notice any number of factors at an instinctual level which will alert her to nefarious individuals. Okay, we all do that at some level. If you are working at a music store and a group of young males with skateboards, baggy clothes, and off-skew hats walk in you're probably going to assume that you should try to keep an eye on them. The problem here becomes obvious. You know that people with these characteristics are more likely to shoplift. Lets say that normally 5% of customers shoplift but that 20% of young males of the type above shoplift. It becomes rational for these characteristics to raise your level of suspicion. Nevertheless, 80% of those with these characteristics are not shoplifting.
Officers are subject to the same sort of process. If they know from experience that they are arresting white males in late model cars on 5th Street (for solicitation and drug purchases) after 8 p.m. it will raise their attention when white males drive on 5th Street after 8 p.m.
Let's say that officer Smith stops a white guy because she has a gut feeling about what he just did down at the end of 5th Street. She finds the typical couple corners of crack. Is the stop good? Well, it shouldn't be. How do we know the number of times she has known "in her gut" that the car driving down the street has drugs in it, stopped the car, and come up empty? Has Officer Smith stopped 22 cars for the 1 time she found something? To be honest, most of the people whom she has stopped are not going to complain to anyone. A 15 minute stop and search is just not all that uncommon among a certain class of our society. There is just no way of knowing. The violations of the rights of several citizens based upon "gut feelings" lead to the arrest of one.
However, if the officer is fairly competent the gut feeling will never be an issue in court. The Supreme Court has ruled that there need almost never be a technical violation of the rights of citizens. Under the Whren, stop 'em for going 36 in a 35 mph zone, doctrine any competent officer can find some amazingly miniscule violation of the law to stay technically within the bounds of the constitution. Of course, they are miles outside of the meaning of the constitution but they are the good guys so we'll let them get away with technicalities. So we're not dealing with Smith's DWW; we're dealing with the "fact" that client had an air freshener on his rear view mirror and the "furtive movement" of the client (you know, reaching into his back pocket for his license as the officer walked up) which leads to the Terry pat down, etc, etc, etc.
That is the level of "gut feelings" which is dealt with most every day by those in the court system. However, there is a level at which it becomes much more disturbing: when officers focus in on your client because they are convinced he has committed a serious crime.
Let's assume that there is a bank robbery and 4 possible suspects. The Detective looks at Jones and knows it's him. The Detective zeroes in on Jones to the exclusion of the other three. He develops every bit of circumstantial evidence he can: height, weight, weapons training in the Marines, etc. Knowing in his heart who did this thing, he does not develop leads which could point to the other suspects. Why look when you know they're not guilty? Or, if he's a more cynical, manipulative type, why develop evidence which a Defense attorney can use to obfuscate the truth?
And you know what? The Detective is probably right in most cases. He's been around doing this long enough that he knows the type of person usually involved in the crime at hand. But if it's that one case where Jones wasn't the guilty party and the officer didn't strongly pursue the report that suspect 3 was doing an unusual amount of gardening the week after the robbery (burying the money in tin cans in his back yard while planting tulips) what is likely to happen is a conviction. Assuming the court appointed attorney is very sharp, finds this particular incongruity, and realizes it is the key to what actually happened, he can ask for an investigator (denied), try to talk to suspect 3 (won't talk to him), ask the officer on the stand why he didn't investigate ("because what's gardening got to do with a bank robbery?") and point out to the jury that suspicious "gardening" took place that week and he thinks 3 might have been hiding something. The prosecutor will stand there and point to Jones' height, weight, training on M-16's (an AR-15 having been used); he will say something about the Defense using smoke and mirrors or grasping at straws. How do you think that case will turn out?