I don't think any third party has the power to choose their visibility, which is kind of my point. If they had the resources of influence (capital) to spend on media exposure they probably would.

Third parties have been trying to gain visibility through presidential elections for decades, and it's been completely unsuccessful.

My view is most third parties are not fielding presidential candidates specifically because you're not wrong: it is not a successful strategy to campaign for that office as a third party.

But moreso, I would refer back to what I said about how most end up as a caucus within the two major parties. In a sense third party politicians have to actively obscure any willingness they have to break from the status quo.

I wager a viable third party would absorb existing key caucuses from the existing two parties, rather than fully challenging and replacing everyone.

Third party doesn't have to be just for the presidency. It generally is anything but that.