One of the most common pitfalls of players in /anything/ is using statistics as indicators. Using rank or winrates to define skill, using card or class frequency to describe balance, the list is endless. One of the most notable application of statistics is looking at a card getting frequent use and thinking "This card is overpowered and deserves a nerf." Let's take a look at why Dr. Boom won't, and doesn't need, a change.
Way back in the day, novice engi was nerfed because it survived too long, able to deal an otk deck's set-up damage by itself. Unleash was changed because of the unfun style it promoted. Defender of Argus, Shattered Sun Cleric, Pyroblast, every aoe freeze spell, Sylvanas, Leeroy, the list goes on. These cards were not changed because they were good, but because they promoted styles that were unfun at little to no cost. Nothing was /ever/ nerfed because it was a high-value minion that was useful in lots of different decks. They only get changed when they hurt the game in significant ways.
Loatheb arguably hurt the game, but he hurt the game because he defended the kind of starts undertaker would let you get. Undertaker also needed a nerf because it meant there was no flexibility in fast-deck construction. If your deck was fast, it had undertaker, and so had tons of other cards. Since that's gone, Loatheb is far less of a concern.
Way before Naxx, every deck ran Azure Drake. It was the best card in the game, to the extent that decks that didn't run spell damage, or a lot of spell damage, ran two of it. There were lots of threads of people complaining about how it was an undercosted, very valuable card, and how it should be nerfed! Hunter appears to be the only exception, but Hunter did not need to because hunter was either nonexistent, or had buzzard unleash.
Why did we stop running Azure Drake as thoroughly as we used to? Because Loatheb and Sludge Belcher were added to the game. Equalizing, powerful, game shaping five drops that could compete with Azure Drake. Some decks do run Azure Drake now, some don't. It's in a wonderful place, as are the other five drops.
Dr Boom is a lategame finishing minion whose main body is significant but vulnerable, and who's effect can sometimes ease the board or provide decent damage, but is weakened by its random factor. Who does this remind you of? Ragnaros and Ysera. Ragnaros had the weakness that he was BGHable, Ysera had the weakness that the effect came next turn at the earliest. Dr. Boom has the weakness of unreliable damage and BGHable body. He also helps unleash the hounds, and makes you more vulnerable to mind control tech. He defines the game after he is played. So does sylvanas. So does black knight. So did cairne, if the match up was slow enough. So does Ragnaros. The list of classic legendaries that compare to him go on.
You don't run Dr. Boom because he's overpowered as shit. You run him because there were no good seven drops in the game. Period. Ancient of Lore is like Azure Drake, a utility minion. Similarly with Guardian of Kings. Archmage Antonidas used to suck, and was next to never played on turn 7, certainly not without coin. Flamestrike is a card that was very frequently overperforming whenever mage was popular, because it was very easy to get good value out of! Why? Because the turns 1-4 are usually all below 4 health, turn five was azure drake, and turn six you could trade with decently to set up for the strike. Dr. Boom provides much needed counterplay to that, as a good seven drop should. Gorehowl is great but slow, baron geddon is meta dependant, and while Stormwind Champion worked in some decks, he was mostly underwhelming. Ancient of War is good, but doesn't do anything when you played it and was as such susceptable to removal. I don't think any other Pre GvG seven is worth talking about.
Dr. Boom is the new Azure Drake. He has nearly singlehandedly caused a huge variety of decks in the meta, has created an environment where every class is to some degree viable, and has left the ladder at the higher stages looking INCREDIBLY varied. Rogues, Paladins, Druids, Hunters, Mages, all in huge amounts, the most varied meta I've ever seen, with Shamans, Warlocks, Warriors, and Priests sprinkled in there at generally consistent frequencies. A good meta pop in the right direction and any of the more underdog classes can quickly become a rising star again. It's how it is, and because of the stability Dr. Boom provides, that's how it should be.
The only problem with him, and it's one blizzard is talking about, is that it's difficult to get him, and to keep up in collecting in general. There shall be a solution to that in time. In the meantime, grind arenas. If you can't grind arenas consistently, you don't have the mechanics to play the game in a way that makes Dr. Boom's balance even remotely relevant. If you don't like arena, then just wait it out. Not even his randomness is that big of an issue, it's no worse than a ridiculous ragnaros shot or some insane knife juggles. That's the nature of the game, and that's the benefit of learning outcome independancy
TLDR: Dr. Boom doesn't hurt the meta in the slightest as every class and every playstyle (aggro, midrange/tempo, control, combo) is currently competitive. Dr.Boom doesn't promote any unfun styles as he's useful in every deck, unlike cards like undertaker which were really good but forced your deck to contain deathrattles, shooting all other fast styles in the foot and painfully pressuring all slow styles. His popular use is akin to Classic's Azure Drake, which was only so widely used because there were so few good fives in the game, and his randomness and resilience is very similar to other legendaries, though also rather appropriately costed. He will see less use once there are more good 7s, but he will continue to see play. Please reduce the crafting cost of legendaries, or increase the amount of dust/gold in the game that's accessible outside of arenas.
Nevertheless, it is a minion that costs 7 mana, gives 3 bodies with a total of 9/9 base stats, two of those bodies have deathrattles that can deal up to a combined 2-8 damage to any of your enemy's target.
Let's see, 7 mana, 3 bodies, total base stats 9/9, deathrattle damage 2-8. What was the vanilla test for a 7-drop again?