The problem is not in "doing" both, but in excelling in both. By excelling I mean literally aiming for the top. This is the only way to advance working ability in a breed, just as competition in conformation is the only way to maintain and advance the appearance standard in a breed. If I said, "Oh, my Border Collies are top notch workers and I believe they would excel if I had the time to show them, therefore they should be accepted as excellent representatives of the breed standard as well" - what would you say to that?
Excellence in the show world means not just being able to win in breed, but also group, and show. The problem we have as working breeders (and supporters of them), is that selection pressure becomes against characteristics that make practical working dogs. The dogs that excel above breed fit the group and BIS judges' notions of what makes a good show dog.
Hunting dogs, terriers, tend to have a little more leeway, especially if they are not coated breeds. What makes a terrific herding dog - sensitivity, reactivity, a reserved nature, a predatory look - these things don't actually "show" well. And so you get the wide contrast between these two dogs, both purebred from the same breed:
A dog bred in Australia where the standard has actually been written to exclude about half of the working breed, to emphasize the "pretty" dogs. These dogs now make up the majority of the top winning North American BCs as well - when the breed was forced into the AKC ten years ago, the standard which favored these dogs was adopted and breeders started importing this stock immediately.

And a dog owned by a good friend, who is a top notch worker and very likely has made a significant contribution to the future of the breed, through a mating to the current cattledog champion (done before he earned his crown, and the pups are showing great promise already).

I know I keep hammering on this point, but I just can't get past the fact that from a show breeder's point of view, my friend's dog would be a cull. There's not a single redeeming quality about her. Ticking is dominant. So are upright ears. So is white factoring. So is smooth coat. All are undesireable to a show dog.
Twist was bred to a beautiful, classic looking stud and here was the result:

It would take generations to fix what Twist would screw up in a show program, and what would you be breeding for then? Excellence in working ability? No, you'd have to look for excellence in working ability among dogs that suit the line, that also would "correct" the "faults" of ticking, upright ears, legginess, slick coats, etc, etc. And do it over and over and over.
It's like starting with the world's greatest basketball team and saying, "Ok, now we are only going to draft red-headed people." How long will we remain the world's greatest basketball team?
If excellence in working ability is not the breed's goal, then that's fine. But it's even written in the Border Collie standard (ha-ha) "world's premier herding dog." So you'd think breeders interested in maintaining that would not be so focused on miniscule variations in topline, head shape, ear set, and markings. And more interested in working achievements greater than being able to move the farm flock around and get instinct test certficates.
Well, you knew where I'd come down on this, lol. It's not that I think every breed should be totally performance focused. I'd just like to see the kennel clubs acknowledge the importance of performance in some of these breeds, rather than representing the breed ring as the be-all end-all.
Edited to replace a word referring to ears, that was censored, lol.