On the subject specifically, I am of the opinion that Look Out Sir should have a localized "HERO cannot be target of ranged attack if nearby friendly unit has models closer to attacker" phrase added to its current ruling. Barring that, I would want bodyguard units like temple guard to confer higher Look Out Sir penalties, either as a horde bonus analogue or as a capped difference between unit model count and maximum hero wounds like what I brought up earlier.
That'd still leaves spells and the issues in melee, but yeah, it'd at least limit the ease with which you can do it. Personally in the current state I'd simply give them a little squad so they can have some ablative wounds as that'd at least stop an enemy from oneshotting them easily, increasing the oppertunity cost and making other targets more attractive. It'd also give a decent excuse for giving them a few more attacks, making them halfway capable of defending themselves. While it'd also leave the fluff of them being minor heroes, only slightly more capable than their underlings. Not superpowered god's of war.
I get the impression you don't get the opportunity to play that many games. It is pretty rare in my experience for support to die without the controlling player being able to mitigate the damage. Especially in the combat phase. It is a trivial matter to pilein in such a manner that the majority of enemy attacks can't reach a hero on a 32mm base if you have other supporting units nearby.
Blocking the majority is obviously trivial, I mean if you have units of 10+ models it's already difficult to get the entire unit in range unless it has 2" attacks, so yeah blocking the majority is trivial.... But also entirely irrelevant if 1 or 2 models counterattacking can already be a significant threat. A skink priest struggles to duel a single liberator in melee combat, only doing an average 0.66 damage and suffering 0.44 damage in return per round of melee combat (not taking into account any potential support). It's completly plausible for that single liberator to take out half of the skink's wounds before he's finished off. And it isn't even impossible for the liberator to actually win. Unlikely, but not impossible (if I'd have to make a guess the skink probably wins 8 or 9 out of 10 times, but he will occasionally lose). That is an utterly terrible trade-off to defeat a single basic battleline model. And that's just a super basic model. Take something slightly fancier like a liberator with a great weapon, or a horde unit with 2" weapons and even protecting the priest like this becomes quite risky.
As for having some oppertunity to mitigate the damage. Sure, you get to stop or avoid some of it. But the moment a minor hero like this gets into range for either melee or ranged attacks/abilities to hit it it's trivial to knock of a significant chunk of its wounds. And again, the only vaguely reliable way to keep them safe is by staying the hell away from combat (or enemy archers, wizards, etc.) which rather conflicts with them trying to actually support. And apart from the fact that staying at maximum range is boring (wohoo, look at my mighty hero, cowering on the other side of the battlefield...), it also doesn't really work as it makes you suspectible to deepstrikes and the like, plus there's no guarantee that your max range actually keeps you out of range for his archers and whatnot...
As for my games, I largely play fairly friendly games, not massivly competitive ones, so we tend to avoid large buffed up cheesy doomstars or super scary behemoths in favor of more fun and manageable stuff to minimize the amount of frustration. This does also mean that support heroes can draw more attention as there's less oppertunity cost to trying to take out at the support, instead of trying to wittle down that huge blob of witch aelves running down the battlefield. There's simply less that needs to be taken care of immeadiatly cuz if you don't take care of it now they'l murder half your stuff and you won't be able to take care of it after that, and consequently we have a bit more freedom to pick your own priorities. Whereas judging from yours and
@Erta Wanderer 's remarks you seem to be playing in a more competitive enviroment with far more doomstars and other nonsense drawing fire away from the minor heroes as most of those cheesy doomstars & behemoths are terrifying regardless of how well supported they are or not.
The Sunblood cost the same number of point as a 5x squad of Judicators. When the Sunblood has the benefit of look out sir it will take an average of 2-3 turns of shooting for the Sunblood to die. That seems reasonable. Sure, you can have 10, 15, 20 Judicators all shoot at the Sunblood and nearly grantee that it dies in a single turn. However, if 2-5x the number of MPP can't be spent to guarantee a unit's death then that is a bigger problem with the game.
A unit of judicators takes on average 33-34 attacks using their skybolt bows to kill another 5 man unit of judicators, not taking into account special weapons, support, or even their captain guy.
A unit of judicators takes on average 14 attacks to take out a skink priest
with look-out-sir in the same setup. Without look-out-sir it takes them 10 attacks.
A unit of judicators takes on average about 33-34 attacks to take out 10 saurus warriors.
A unit of judicators takes on average about 28 attacks to take out 10 skinks with shields
Why is a skink priest so much easier to kill than basic battleline and even cannonfodder? Even with the additional protection of look-out-sir he still dies in less than half the attacks needed for the judicators & warriors and about half the attacks needed for freaking skinks. None of those are even particularly sturdy battleline. Without the additional protection he barely takes a third of the damage any of the others need.
Also, I actually think the sunblood is more or less fine defensivly, or at least in a vastly better spot than the skink priest. He isn't a support hero, he's a combat hero and actually has fairly decent stats. If you're interested it takes something like 42 attacks for the judicators to take him out when he has look-out-sir. Any buffs he needs defensivly are purely to deal with powercreep, not because he's inherently designed to fall over to a stiff breeze like the skink priest is. It's his offensive where I'd like to see some buffs (the exploding dice give him a nice potential, but he's completly reliant on those 6's so a mediocre round can see him doing very little)
again heroes are far to powerful to be invinsable like this no one can kill a 30 man unit of hearthguard when they are buffed even Gotrek takes 2-3 turns so you need to kill the rune master. what happens if you can't shoot him because he ether can't be targeted or he has a -3 to be hit. you can't break thru the berserkers as stated above you have to shoot him or play much better then your opponent everything in the game needs counter play sniping is just one of them.
That is not a support issue though, that's an issue with hearthguard being stupidly powerfull baseline. Hell, the things that make a hearthguard powerfull are all on their own warscroll. The "support" doesn't even need to do anything besides exist, it doesn't even need any abilities or rules of its own, for the hearthguard to become problematic. So that's really not an argument against improving support. It's an argument in favor of lowering the baseline power of these kind of units.