Quote:- "...what about 苦苦...."
As for why isn't 苦苦 equate to "double bitterness", well, 囍, "double happiness", is more a single-event occurrence due to the specific circumstances as told in the back story of the scholar, (and thus an "artificial concoction", a runic symbol rather than a legitimate word. Therefore, only 喜 is a legitimate word.), and so it is not correct, linguistically speaking, to equate 苦苦 as "double bitterness"
Thus, 苦苦, unlike 囍, is therefore coupled with another double, 辛辛, making it, 辛辛苦苦, (lots & lots of hardship), to make it in a sense, "double bitterness", or "great hardship", like, 我父母辛辛苦苦地养大了我.
However,辛苦, by itself can be used as 她很辛苦的赚了一些钱. Here it is more about having to put in great effort, rather than "Hardship"
Also, the word 苦 has much socio-cultural significance for the Chinese who seems to see "hardship" as a positive facilitator of a person's character. So, we have words like, 吃苦, literally to "eat bitterness", meaning that by "enduring / eating hardship", one either becomes a better person or makes great achievements.
As for 喜, there is another way of saying "Double Happiness--囍", in the idiom, 双喜临门, meaning something like "Joyous events comes in twos or all at the same time" The 临门, meaning "at our doorstep", is to say these multiple joyous events come all together to our door / homes.
Or, to say 喜上加喜 to emphasize the "doubling" or "adding more" of happiness.