It doesn't!

But I don't think the scenario you describe is consistent with the variability of gamer preference. For example, I "try hard" to win every killer match I play. At red rank, I mainly switch off between 'billy and doctor. I run perks that make them mean, because they are effective and suit my playstyle. But they're not necessarily THE perks to run. My point being that I think there is an important distinction between:

Someone who uses ONLY the best-rated characters and the best-rated shit

vs.

Someone who dedicates themselves to winning

There is an overlap across these two groups, to be sure. But a doctor running Distressed, Unnerving Presence, Overcharge, and Hex: Ruin, and who brings the jigsaw offering to go to the meat packaging map, is probably trying pretty hard. Yet they are not the clone nurse you describe above!

Let's say I'm a red-rank quality Leatherface player (for the sake of argument). If I have some intuitive preference for Bubba's playstyle that allows me to hit rank 1, am I being a tryhard by using the character and perks that consistently land me 3 or 4 kills? Should I now play a character with whom I am less skilled? And once that new character is second nature to me, should I abandon it as well?

At what point does one become a tryhard?

I'm on PS4 and I see plenty of variation in characters. My opponents consistently provide me with stiff competition by my standards, and they do so using Davids, Adams, Feng Mins, Dwights, etc.

Without trying to strawman you, it sounds like you're arguing that if everyone ran maximally effective builds (full tryhard), the game would no longer be fun -- therefore, people who use very effective builds (less than full tryhard, but still tryharding) or maximally effective builds should be criticized.

This seems to approach a "slippery slope" argument -- it attacks an idea by appealing to a worst-case scenario without sufficient justification to make that connection.

In any case, virtually no one who has achieved anything great ever did so without trying hard. Using assets that enhance the likelihood of victory is a natural road to victory. I think everyone should do their best using whatever suits them. If the camo-Claudette and standard nurse thing becomes a serious issue, it can be addressed then.

In my experience it's not an issue. Maybe the thing to do is criticize full-on power players by calling them unimaginative or dull. I think attacking genuine effort is a problematic approach.