Is there a way to make [High Resolution] the default for Transparency when saving as .eps

Did you ever get an actual answer to this question? As I need to change this setting because the rip software we use for work only allows EPS formats & I believe it is this resolution setting that is generating sawtooth edging on our gradients as all other settings have been adjusted to high resolutions. Also How is Jeffs answer in anyway constructive to the question that was asked. The fact a moderator came along & marked it correct is astounding. Not only is it not correct it's entirely unhelpful. Pretty sure we would all ditch EPS formats if possible, but unfortunately its not. & pointing out that "AI" is better is either covering for the fact that you don't know the answer but due to a lack of attention as a child feel the need to insert yourself into the conversation. Or you are truly lacking the cognitive ability to understand the difference between constructive communication & just stating the overwhelmingly obvious.

Would love for someone to actually answer the original question if possible & as I feel it needs to be stated, I am not looking for your opinion on why you don't like EPS or what you feel is better or any other inconsiquential thought that happens to wonder into your mind. Just how to solve the issue. So lets stick to that.

You might mean «Raster Effects» instead of «Transparency»? But @Jeff_Witchel__ACI was right.

If you go to File > Save As and choose Illustrator EPS, you'll notice that the Transprency Preset is grayed out. That's because there is not Transparency in the EPS format. It does not matter what the Preset is by default, there will be no Transparent Effets in an EPS.