There's no reason to show that you're pinging your allies' summoners, items or ults. None.
The option to ping pretty much everything, was a cute little novelty. But honestly, really think about it. What benefit is it to show the entire team that you're pinging their ultimate? None. If you click an ally's summoner/ult/item it should just be for you and you alone. There's no benefit to this option. All people ever use these for is one thing. Spamming something you don't like on your ally.
Your ally has heal up and you died? Ping the heal summoner 50 times. Your ally has a build that YOU think is odd and troll? You ping it 20 times. You think that they should have ulted that losing 2v5? You ping spam their ult while you're dead. I can go on and on and on about how pointless this option is, but you get the point.
Fine, you genuinely want to ping your ally's ultimate to see what the cooldown for it is, cool. It should only show up on your screen. Or anything you ping on your ally.
The only benefit to pinging your ally's item/ult/summoner is that you know who's raging the hardest.