I play a main spec healer in a casual raiding guild and thus I have all the gear I need from LFR for my healing spec. This has been the case for quite some time. I do not, however, have anywhere near a full off spec set of gear. I run my LFRs most weeks, but half the time I queue as a healer and just dps, while the other half I queue as dps. These two scenarios are indicative of the two biggest impediments to healer participation in LFR. An simple option to chose the spec you want LFR gear from instead of being forced into gear from your current spec would absolutely encourage me to heal a greater number of LFR bosses. This would help with other healers as all healing classes have at least one off spec set of gear.
Further exacerbating my lack of participation in LFRs as a healer is that it is incredibly boring. LFR damage is so under tuned that there is very little to do as a healer. DPS can still watch meters and blow stuff up, tanks are still managing adds and working with fight mechanics, but healers do nothing. I have found no correlation between the success of runs with 6 healers versus runs where I am supposed to heal but dps instead.
LFR needs to be incredibly easy in comparison to an organized guild run, however, the developers needs to take a look at tuning these in a slightly different fashion. It is necessary that abilities which one shot a character in normal mode do not have the same massive damage amounts in LFR. This allows inexperienced players to make mistakes and have fun. Examples of such abilities would be Spirit Kings Anihilate and wind bombs on Windlord. However, pulsing aoe damage and standard tank damage just does not need to be as low as it currently is. LFRs need to be tuned such that a failure to execute raid mechanics does not kill the group. However, damage that is not tied to a raid mechanic should be much higher so that there is sufficient incoming damage to provide healers with something to..... heal. If there is nothing to heal, it is not fun to be a healer, and healers will not participate in LFR unless they need heal spec gear on that particular fight.