If I had to think about Pichu...
First and foremost, his range stinks. Despite the existence of Jolt and Thunder (and Thunder barely counts...not sure how you combo from it...) pretty much all his moves have tiny hitboxes. I challenge anybody to prove otherwise, because I seriously don't know any move that would have "priority" over...well, anything not Pichu.
He's decently fast, but I have never once seen that speed properly compensate for the lack of range. On this point, I'm definitely no expert because I try spacies and say "Wow, what crappy range". Yeah...whole reason I main Marth...
Self-damage is actually pretty minor...unless you're spamming Fairs, I don't see how it becomes a significant issue. But really, don't use that Fair: high self damage for hardly any output. And why bother when you can just chain Nairs like Marths chain Fairs?
Maybe another issue is that his Tilts are so stubby to the point of unusable? Not too sure what to think of this, but last I checked they all use his tail. And his tail barely extends past the regular hitbox. The jab is still pretty good but everything else can barely be considered usable. Ok fine, so his Ftilt uses his legs...his just-as-stubby legs.
Following that, predictability? Pichu's approaches are more or less limited to Jolt and Nair/Bair. Well, maybe mindgamed Thunders, but that's pushing it. Anything else would be way too easy to read and Pichu has more traction than I'd like...making any sort of wave-move use difficult. Maybe a JC USmash, but even that's pushing it since you pretty much have to be inside the target.
I'm not too experienced, but that's my 2 cents.