Suckerbombs and splat bombs (w/e they're called), make this little area that enemies have to move from/can't walk on. Burst bombs just throw some ink out for some mediocre damage and ok ink coverage. I've never really been killed by, or had my movement affected by, burst bombs in any manner a suckerbomb/just shooting me wouldn't have done.
Exception goes to chargers who can actually have some solid AoE damage by mashing RB which can be situationally very useful.
It sounds like you haven't seen anyone use them optimally yet.
Three Burst Bombs uses the same amount of ink as one normal grenade. If you throw three Burst Bombs it denies the same amount of space for the same amount of time. This is bad because you have to keep looking in that direction and not shoot. This is good because it gives you more options. For example, if I know someone is going to backpedal when they see my first bomb hit them, I can throw the other two behind the first one by jumping when I throw, and if one of the others catches him I get the kill. I kill Chargers and Squelchers like that all the time. You can't do that with the other grenades.
Damage Ups change the burst bombs completely, because it takes them from doing mediocre damage to leaving whoever you directly hit weak enough to die from one shot from almost anything. The splash damage is strong too. This is good for 1v1 fights because you can retreat and throw a bomb after you see one hitmarker and get an easy kill. When both teams are firing at each other and a few burst bombs get tossed into the mix, people start dying. This is a threat because you can throw them so often.
It only takes 2 subs of damage up to accomplish this, or more if you're worried about enemy defense ups. That's one of the primary problems with the Splattershot, you NEED Damage Ups to be viable, so there's an opportunity cost of other abilities the more you invest.
I don't think the Splattershot is top tier, but it's high tier. It doesn't have a good enough Special to be top tier. It's definitely not mediocre or bad though, even if people aren't using it properly yet.