This is more of a question for the Strategies & Movesets section, and we will probably get warned by a mod, but I will explain it anyway.
Blissey is simply one of the best Pokes in the game. Before I can explain why, I need to explain a BIG difference between battling in-game and through link or Net Battle (online). In-game, against the pathetic AI, it will RARELY (and I mean it) ever switch out its Poke if it gets statused (i.e. SLP, PSN, BRN, etc.) or if it is facing a severe weakness (it has Onix out and you bring out Swampert). What this does is train the person to behave the same way. That is horrible strategy, but the AI is set up that way in order for younger kids to be able to progress through the game without losing too much interest. So those of us with higher than a fourth grade education level are left wanting, wishing that Game Freak would instill some sort of difficulty level.
Now, when you play against someone else (whether it be a link battle or online with NB), a good player is going to immediately switch out to a different Poke that will either resist the Poke you have out (i.e. switching out Onix for Milotic), or to a Poke that your own Poke has a weakness to (i.e. switching out Onix for Sceptile). What that does is make your pending Surf attack not very effective. These type of battles causes, or rather FORCES, you to learn good strategy and how to predict what your opponent will do. Well, unless you enjoy getting your butt handed to you all the time.
So, where does Blissey fit into this? Simple. Because of the ridiculously high base HP and SDef that you alluded to earlier, you can switch it in against a powerful special attacker (like Alakazam or the Gengar used in my above example) and stop it dead in its tracks. In my above example, Gengar would NEVER be able to KO Blissey. Why? Because its attacks can only do 8% max damage to it. So, after a few hits, Blissey uses Softboiled and heals it s HP all the way full again. Gengar will eventually run out PP before Blissey even comes close to having below 50% HP. Not only that, but a good Blissey will also be equipped with Ice Beam and either Seismic Toss or Thunder Wave. Ice Beam, despite Blissey's very average base SAtk of 75, can still dish out more damage against Pokes that don't resist it, than it receives itself. It will OHKO Salamence with some SAtk EVs and it can also do 34% max damage to Gengar, while Gengar only does 8% to it. Seismic Toss is another good move since it inflicts damage that equals the level of the Poke using it. That means ANY Poke in the game that isn't immune to it, will lose 100 HP to Seismic Toss. So, unless your Poke or your team has some way to replenish HP, Blissey is going to slowly defeat your entire team.
Thunder Wave is more of an annoying status move that a Blissey user will use to inflict as many Pokes in your team as possible. So, unless you have a cleric on your team (a Poke with Heal Bell or Aromatherapy), your Pokes will be at a disadvantage, having to go last each round and subjected to a 50% chance of not being able to to attack at all.
What about its EXTREMELY low Def (base Def of a pathetic 10)? Yes, that is definitely an issue, but with a proper nature (Bold) and maxing out Def EVs and almost maxing out HP EVs, an Earthquake from Salamence will only do max damage of 37% to Blissey. Salamence with Brick Break also only does max damage of 56%. A STAB Meteor Mash or a STAB Earthquake from Swampert doesn't do much more than that. To be honest though, against Pokes like that you would switch out your Blissey for a Poke that can resist physical attacks like Blissey does special attacks. A great example is Skarmory. You switch Skarmory in against Salamence that uses Earthquake, Earthquake misses because Skarmory is a metal bird, and then you can either set up a Substitute or put down a layer of Spikes while your opponent typically switches out to a Poke that can hurt it.
So, as you can see, Blissey is definitely a Poke that you need to prepare for. Thankfully the AI in the Battle Frontier doesn't maximize Blissey's potential like that. Crappy Double Team always fails.
Hope that helps.
BTW - I failed to cover what else Blissey can do. It can remove any status that your team is inflicted with, during a battle. This is yet another difference between in-game and link/NB battles. When you battle in-game, you have access to all the items in your pack. If one of your Pokes gets put to sleep, you take a turn to wake it up with a Poke Flute, Blue Flute, Chesto Berry, or Awakening. In a link/NB battle, you don't have access to any items. The only way to counter statuses is to either prevent them (Safeguard prevents statuses for 5 turns) or cure them (Heal Bell and Aromatherpy will remove all statuses your team is inflicted with. You also have the Natural Cure Trait, where when the Poke is removed from battle, it is cured of any status. Clerics are pretty valuable to the makeup of your team.
For example, if you have Salamence out and it gets hit with Will-O-Wisp, not only will it take damage each turn (1/8th of HP, iirc), but it also halves the attack of physical moves. Unless it is holding a Rawst or Lum Berry, it has just become ineffective. It will only do half the damage it normally could. With Blissey on the team, you would simply switch it in, use Heal Bell or Aromatherapy, and remove the BRN from Salamence. Now at full strength, Salamence can now be a force to be reckoned with once again.