Second, in my view, the DM does have a say on what classes and races are in the party. Specifically, the DM decides up front which classes and races are available in the campaign world. The players are free to choose from the menu of options the DM offers, and the DM shouldn't try to dictate who picks what; but the DM chooses what goes on the menu in the first place.
I prefer to approach it as a much more collaborative problem. In my game, I told my players that my version of the Nentir Vale was populated primarily by humans, dwarves, and tieflings, which are the cultural remnants of my Bael Turath, so they should consider those races in particular. However, there's also a large orc and half-orc population in Hammerfast. Elves live in a not-too-distant region, and are common enough to not be exotic but still be obvious foreigners. Eladrin live off in the Feywild, but most people can't tell the difference between a visiting one and an elf anyway, and if one of their gnome slaves escaped, the mortal realm seems like a great place to run to. Halflings are nomadic, so they could turn up. If they wanted to be a dragonborn, we could work out a backstory as to why they're here from the southern continent that once housed Arkhosia. If there was anything else they had their heart set on, such as other near-humans like shifters and goliaths, we could talk to work something out, but I frowned on bizarrely alien things like shardminds.
The end result is a party with two dwarves, a human, a tiefling, and a elf. My wife wanted to play a dwarven swordmage, so her dwarf is mechanically an earthsoul genasi. I've now developed backstory about caste divisions between dwarven nobles like her and commoners like the other dwarf, and they occasionally have a bit of friction over that. Meanwhile, the tiefling actually looks more like a firesoul genasi, after the player waffled around a bit during creation, which I've worked in as one of the lesser-well-known houses of Bael Turath, descended from flame devils; the commonly-known tieflings are from House Tief, which survived the fall of Bael Turath better than the other houses, having previously relocated to the captured dwarven city of Bael Modan, which became a secondary capital afterwards until its eventual fall (not unlike Rome and Byzantium).
4E stepped back from this, which I find sad. Essentials has given humans a significant power-up with Heroic Effort, but I would have preferred to see them get a second floating stat bonus instead. The fact that you can't get +2 to both your primary and your secondary stat is a significant drawback for humans; if they had two floating stat bonuses, humans would once more become the "do-anything" race suitable for almost any build.
Even before Essentials, humans were still really good. A lot of classes don't care that much about their secondary attribute, and the +1 to all NADs humans get often more than makes up for it, before considering their extra feat, extra trained skill, and extra at-will. At the game's release it wasn't so impressive, but the value of that extra feat continues to go up as the number of must-have feat taxes increases. Being able to drop that not-always-useful third at-will for a per-encounter retroactive die boost makes them even better. Unless you're considering a class and build who wears light armor and whose secondary attribute is their armor attribute, humans are usually a top choice for every class. People just underestimate them because they have a large number of small bonuses, instead of one big amazing thing to point to.
