When you say "don't like" I would have to to ask, for what? For a field rifle they can be just fine. I have one in .222 that does a good job. If however you are talking about competition from the bench, there are several reasons that I would not pick a Winchester action as a starting point for a Benchrest rifle.
Lets start with resale. All the non action costs will be the same as for any other action. If you built a 1,000 Benchrest rifle on a Winchester, the chances that someone will give you a good price for it when you decide to move on is about nil.
Next, let's look at design. Because the width of the locking lugs is narrower than a Remington, giving direct support of fewer degrees of the case head, no less an authority than the late Creighton Audette opined that this resulted in reduced accuracy potential. Also, it has been demonstrated that the smaller tenon diameter (1" vs. 1 1/16") causes a tight bolt to occur at lower pressures with large diameter cases.
Now let us turn to bedding. The shape of the Winchester tang ( a critical area in bedding because of the forces exerted on such a small area) is not a good one in terms of effective area to be bedded, as well as the shape of that area as compared with that of round actions.
Next, let us look at gunsmiths. As far as I am aware, there are no gunsmiths that have experience in building a winning Benchrest rifle based on a Winchester action. This alone should send up a flag. Truing actions to Benchrest standards requires tooling that is adapted to the task. Most of the available tooling is for round actions. Finally, you should consider the availability of aftermarket parts such as stocks. While it is true that almost any stock could be adapted to a Winchester, this would require additional work, increasing the cost of the rifle. There are probably other reasons that I have not thought of, but these should give you a start.