Great Question; with two very good points.
This is my interpretation.
Since handlers are only considered wound counters for the unit, skinks can be regrown; skink wounds are really just salamander counters.
The rules states about salamanders;
lizardmen pg. 56 "If all the skink handlers are slain, then the remaining salamanders must take a leadership test, and if this is failed, roll on the monster reaction table".
Since the Monster reaction table is also very clear about what happens, if you roll:
-1-2 "uh" Monster fights on as NORMAL {hence handlers can be revived with good effect}, but, is subject to STUPIDITY FOR REMAINDER OF GAME.
-3-4 "GRRRRR" Monster is UNBREAKABLE. The monster WILL NOT MOVE FOR THE REST OF THE GAME, except that it will always turn to face towards the closest enemy in its movement phase and use any breath or other ranged weapon against the closet enemies within range if possible.
{so not an effective target to bring back in my opinion}
-5-6 "RAAARGH!" The monster fights on as NORMAL, but is subject to FRENZY AND HATRED of all enemies for the REST OF THE GAME (it can NEVER LOSE FRENZY), and will ALWAYS CHARGE closest Eligible target.
{So great! I can res. my handlers and go smash into someones flank!}
BRB pg. 106
So when your monster takes a reaction test, its a crap shoot as to if you want to bring handlers back. You always can- don't always want to.
Also, RAW if you res'd back one handler, just have to have him killed, the salamander would once again have no handlers, and once again would need to test to not roll on the table, and if he reacts would add another reaction: assuming you rolled something different.