My own attempt at answering this question was to think for at least 5 minutes of ways in which a society could possibly avoid its people having their hearts broken, and evaluate the solutions on a do want/do not want scale.

The first method would be to never let anybody fall in love again. Either humans would be modified such that they would never feel love again, or they would be isolated such that they could never interact with the appropriate gender (so... straight men with each other, straight women with each other, gay men and lesbian women in single pairs, bisexuals by themselves, etc... if not just isolating everybody individually). This strikes me as completely unacceptable.

The second approach would be to avoid heartbreaks once a person has fallen in love. We consider the cases where a person might have his or her heart broken after that event: the other person might reject them initially, lie to them and string them along until revelation, love them back for a time but eventually stop feeling the same way and leave them, do something that causes first person to leave them while still being in love themselves (cheating, spousal rape, etc...), or be separated from the first person due to circumstances beyond control (death, physical separation due to economic circumstances, etc...). At least, those are all the ways I can think of.

Hopefully, by the time we can seriously talk about eliminating heartbreaks as an implementable policy, the latter will no longer be a serious consideration for people. The case of lying could be taken care of if humans were prevented from lying somehow, either in a specific case (humans can't lie to their partners while in a relationship/can't lie when saying "I love you"/some other constrain) or the general case (humans can't lie at all); I must admit that the former seems to me mildly attractive depending on how it is implemented. To handle the case of people falling out of love, humans could be modified such that they never fall out of love once they have become enamored of someone who loves them back and they have become lovers. This is definitely interesting; I can't see any immediate objections to that one that aren't part of the fully general "ick! You are changing me and taking away my free will" reflex. The rejection case could be solved by making it such that people reciprocate love once someone has fallen in love with them, maybe even changing orientations to do so; I don't really like this one. Comparing it with the last case discussed, the difference seems to be the difference between making a change and preserving a state; I'm not sure this is something I should care about much, so I will consider it more fully later. And the last case... oh, hell, I don't know. I don't think taking away the ability to do such things works without also removing the intentions, unless their partner never finds out about them.

The third way would be to let people fall in love, but only with people who would not break their hearts. It seems like creating human imitations who would always love one, a la Failed Utopia #4-2, is one possible venue of attack. It also looks like some ideas from the second set of situations coulde be re-applied with a bit of tweaking...

Aaaand I'm gonna stop there, because I just realized that on top of this, I have to consider all the cases for the polyamorists, too. Jesus Christ, people are complicated; Randall Munroe was right. Sorry if this seems confused, but that's mostly because it is; this is the first time I have seriously considered the problem. Still, I hope to have contributed something with my post.