The halachic issue behind broiling liver is the prohibition to eat blood (Vayikra 17:10). "Since the liver contains much blood, it therefore not permissible to cook it even after salting it" (quote from SA YD 73:1, see also here).
Maybe less well known is the fact that the heart also cannot be eaten after only being salted and cooked. Blood first needs to be removed from the heart by tearing it open, washing and salting it.
HalachaYomit brings the following
Heart is sold in stores without being koshered first and there is
still blood in it and it may therefore not be consumed until it
undergoes a halachically valid koshering process. The reason why heart
is not salted before it is sold is because when the animal or bird is
slaughtered, a large amount of blood is collected in the heart and it
is like a container for this blood and it cannot be expelled through
salting alone. Thus, even if they would salt the heart, this would not
be sufficient to release the blood contained in it and consumption of
the heart would still be absolutely forbidden.
Before the heart is salted, it must be torn open and the blood inside
it must be washed off with water and only then may it be salted.
Tearing the heart refers to cutting it at least once deep enough that
it reaches all of the corridors of the heart along either its entire
length or width. [...]
After doing so, one should salt the heart well by covering it with
fine cooking salt on all sides and leave it in this matter for
approximately an hour on top of a rack or other perforated utensil so
that all the blood can drip out of it.
If one does not wish to salt the heart (or any other piece of meat for
that matter), one may kosher it by grilling it (preferably, one should
place a small amount of salt on the meat and only then grill it) since
grilling also causes the blood to flow out of it and it will then be
permissible for consumption. Even when wishes to kosher the heart by
grilling it, one must tear it properly as we have explained above
regarding salting the heart.
So it is really the presence of blood in blood-rich organs, such as the liver and the heart, which is the root issue.
There remains a key difference between the liver and the heart. One can take blood out of the heart by tearing, rinsing, salting then cooking it (see here). For the liver, one needs to tear or slice, rinse then broil/gril it (see here and there).
I imagine the difference is that blood gets more absorbed into the liver than the heart. @JoshK in comments speculates it is because of the density of the liver. But I don't feel qualified to comment on the science of it (and am not sure it belongs on this site).