I tend to avoid the word "compassion" altogether. It's etymology is sticky. The word is rooted in ecclesiastical Latin, and specifically alludes to the "co-suffering" of the Christ with the rest of humanity.
Agree, that's part of the history/origination of the word. But that's very old history. It doesn't mean that in today's usage. Words change in meaning over time and there is no other word that can replace it today and have the same meaning. Pity and empathy and sympathy just don't fill the bill (and most folks don't know the history of all this anyway).
since "compassion" (or "co-suffering") necessarily includes the idea of "suffering", I think the word is antithetical to the Epicurean goal. A wise person would not contribute to their own suffering by accepting the same punishment as someone else; rather, a wise person would direct their efforts toward trying to remedy the situation
I can totally understand your perspective Nate, as this seems counter-intuitive. But I have lived through this and can honestly attest to the fact that cultivating compassion can be a very positive thing. This is an example of accepting some pain (the extent to which we can take on the pain of someone else, limited) to gain at least 2 greater pleasures 1) a very powerful pleasure of helping someone, and 2) more broadly the pleasure of deep connection with people. This is very meaningful work. Enjoying the good fortune of a friend for instance, is a great thing, but if you help a friend out when they are truly suffering, the connection is much deeper and more powerful. Same with non-friends (in fact sometimes friends are made this way!)
That said, compassion CAN be problematic - it depends on the details. One can become overwhelmed by compassion (we've all heard of this among health care workers during this pandemic, as just one example). Also some persons are so sensitive (or even have outright medical/psychological issues) that most any effort at compassion could be debilitating or even dangerous!