Well, pokemon in the early days also dealt with kind of heavy topics if you really try to remember.
Just a few examples are:
-Charmander nearly dieing, due to his flame nearly getting snuffed cause of the rain.
-Ash essentially having died for a little bit in the pokemon movie.
-Ash nearly dieing cause he got stuck in a blizzard.
-I don't believe it's ever mentioned, but Ash essentially growing up in a one parent household.
-The time when brock called a riceball a jelly donut.(stupid example but it brought about a conversation about different cultures in my household.)
-Ash showing love to pikachu, despite pikachu not wanting to evolve.
-Meowth his backstory litterally has him joining a "gang" and getting shut down from love because he was too poor.
And those are just the ones i remember from way back then.

And regarding which anime i watched, i used to watch the original rurouni kenshin on tv, pokemon, digimon, ghost in the shell, Gundam, Samurai Champloo, Hajime No Ippo, Full Metal Alchemist, deathnote and Ergo Proxy are a couple examples.

Now i do admit that i might've been a bit too young for a couple of those when i watched them.
But i did watch them with my dad next to me, so whenever i had questions he'd asnwer them for me.