The sorcerer isn't so much broken as it is overshadowed by the wizard. In 3e, the sorcerer was the poster for spontaneous casting, being able to use their spell slots for anything they knew how to do. So a 3e wizard could do anything, but they'd have to decide in advance what they wanted to do that particular day, whereas the sorcerer could just do their regular stuff. In addition, the sorcerer in theory had more spell slots than the wizard, though the difference in practice was less than advertised on account of specialization and gaining spell level access one class level sooner.
But in 5e wizards are much more flexible, because of the differentiation between spell slots and spell preparation. If needed, any wizard can spend all their slots on fireballs, but if not they can use them for haste, Leomund's chest, and so on instead. I really like that from a wizard point of view, but it does impinge a lot on the territory that used to be the sorcerer's. It certainly doesn't help that a wizard will likely have between 40% and 100% more spells prepared than the sorcerer has spells known.
That leaves the sorcerer with sorcery points, which they can use for two things: spell slots and meta-magic. Using them for additional spell slots is approximately as good as the wizard's Arcane Recovery ability, though the latter requires a short rest. So only meta-magic remains, and I don't really think meta-magic is good enough to match against having half-again as many spells ready at your fingertips, with potential access to many, many more.
Looking back at the playtest, it appears that they struggled quite a bit with what to do with the sorcerer. I remember one packet that had the sorcerer as a warrior/mage hybrid that became more draconian the more magic they used (so they'd start the day with full access to their magic, and by the time they had used that up they'd kick ass in a fight instead) - that was a nifty idea, but pretty far from the sorcerer we remember from 3e so they kiboshed that. In the final playtest packet (september 2013), they didn't even have sorcerers or warlocks, having gone back to the drawing board on them. So the sorcerer we have in the PHB has received a lot less playtesting than the wizard, and it shows. I think that given the lack of playtesting, they wanted to err on the side of low power with those classes - and that was probably the right call, since a slightly underpowered-but-flavorful class is at worst a waste of pages, but an overpowered class can break the game.
And leave the old class to those that can enjoy it.
