Am I understanding BFS/IFS correctly?

Apologies, I've read a bunch of posts here trying to understand, but sometimes things just don't click for me. Could you help me make sure I got it right?
I have a Typhlosion right now with:

• LV10 BFS
• LV25 IFS
• LV50+ Helping Speed S and M, Skill Trigger S

He's the only Cyndaquil line pokemon I have, which is one of my favorites so I'm going to be using him, regardless.
But if I understand BFS and IFS correctly, they're going to make him fill up his inventory very fast. And when his inventory is full, he will no longer have chances to use his main skill. So he is going to require frequent baby sitting. Is that right? There's not really any other downsides to him having those skills, right?