I have 21 Platinum Trophies, which admittedly aren't very many in the grand scheme of things, but I love going for them. That being said, I only chase Platinums when I know I can obtain them without massively affecting my gaming style.
Getting all secrets and A+ing all levels in Hotline Miami? Sure! Otherwise I would have played each level once and moved on. All weapons in Bloodborne? Sure! It rewards exploration, so that's a plus. In most cases, a Platinum for me is a "medal" that I get for completing a game I really like.
Now, there are some games that are decidedly impossible for me to get Platinums on. Most games with multiplayer Trophies (like PlayStation All-Stars Battle Royale), or games that you have to beat on a brutal difficulty level (Divinity: Original Sin or XCOM)... Nah. I don't go after the Platinum for those games. I just play them and enjoy the experience for what it is, then move onto the next game. There's no point in forcing myself to play those games as a completionist if I'm not going to "complete" them.
Ehh... Kinda have to disagree. There's very little objective value in video gaming. You could argue that with any game you could be doing something else that would be more "productive". Besides, if you spend 100 hours playing a multiplayer game, is that worth it? Or is it only a waste of time if you're chasing a Platinum Trophy?
I wouldn't judge any hobby as a "waste of time", regardless of the time invested in it. The only reason for saying that something is time wasted is that you are actively not enjoying what you're doing and you're not getting anything from it.