The way I see it, a race's write-up in the PHB is supposed to provide you with some ideas of the typical heroes and adventurers for that race. Of course, players can and do come up with their own ideas for heroes and adventurers of all races, and often, it can be fun to come up with a character that subverts the expectations of that race. My criticism of halflings as presented in 5e is that their racial write-up doesn't really do that. Let's compare the halfling write-up in the PHB with the write-ups of elves, dwarves and gnomes for each of the 13 classes.
1) Artificer
Elves: No mention.
Dwarves: No mention.
Halflings: No mention.
Gnomes: "crunch of grinding gears, minor explosions...", "many gnomes are skilled engineers, alchemists, tinkers and inventors", "homes are well-hidden with clever constructions...""Gnomes who settle in human lands are commonly gemcutters, engineers, sages or tinkers", "those who tend towards law are sages, engineers, researchers, scholars, investigators or inventors".
2) Barbarian
Elves: No mention.
Dwarves: No mention.
Halflings: No mention.
Gnomes: No mention.
3) Bards
Elves: "...soft music drifts through the air...", "Elves love nature and magic, art and artistry, music and poetry...", "Elves encountered outside their own lands are commonly traveling minstrels, artists..."
Dwarves: No mention.
Halflings: "fine drink and fine conversation", "Halflings are an affable and cheerful people", "Halflings are adept at fitting into a community...making themselves valuable and welcome"
Gnomes: "Gnomes take delight in life", "those who tend towards chaos are minstrels, tricksters..."
4) Clerics
Elves: No mention.
Dwarves: "Part of their traditions is devotion to the gods of the dwarves, who uphold the dwarven ideals of industrious labour, skill in battle and devotion to the forge", "Other dwarves are driven by the command or inspiration of a deity, a direct calling, or simply a desire to bring glory to one of the dwarf gods"
Halflings: No mention.
Gnomes: No mention.
5) Druid
Elves: "They live in the midst of ancient forests", "Elves love nature and magic", "Like the branches of a young tree...", "They have been known to retreat from intrusions into their woodland homes", "Most elves dwell in small forest villages hidden among the trees. Elves hunt game, gather food, and grow vegetables, and their skill and magic allow them to support themselves without the need for clearing and ploughing land"
Dwarves: No mention.
Halflings: No mention.
Gnomes: "Forest gnomes are rare and secretive. They gather in hidden communities in sylvan forests, using illusions and trickery to conceal themselves from threats...", "Forest gnomes tend to be friendly with other good-spirited woodland folk", "they also befriend small forest animals"
6) Fighter
Elves: "elves reveal a stern martial side, demonstrating skill with sword, bow and strategy", "nobles compete for services of elf instructors to teach swordplay or magic to their children", "elves enjoy exercising their martial prowess"
Dwarves: "dwarves are known as skilled warriors", "who uphold the dwarven ideals of skill in battle", "some become mercenaries or bodyguards, highly sought after for their courage and loyalty", "a dwarf might search for the axe wielded by a mighty ancestor, lost on the field of battle centuries ago".
Halflings: No mention.
Gnomes: No mention.
7) Paladin
Elves: No mention.
Dwarves: See quotes for fighters and clerics.
Halflings: No mention.
Gnomes: No mention.
8) Monk
Elves: No mention.
Dwarves: No mention.
Halflings: No mention.
Gnomes: No mention.
9) Ranger
Elves: "like branches of a young tree", "elves reveal a stern martial side, demonstrating skill with sword, bow and strategy", "elves hunt game, gather food and grow vegetables, and their skill and magic allow them to support themselves without the need for clearing and plowing land", "nobles compete for the services of elf instructors to teach swordplay or magic to their children".
Dwarves: No mention.
Halflings: No mention.
Gnomes: "Forest gnomes ... gather in hidden communities in sylvan forests, using illusions and trickery to conceal themselves from threats...", "Forest gnomes tend to be friendly with other good-spirited woodland folk", "they also befriend small forest animals"
10) Rogues
Elves: No mention.
Dwarves: No mention.
Halflings are in a weird position in that unlike all the other races listed, their write-up suggests that are they less likely to be rogues, even though it makes sense mechanically: "wanderers love peace, food, hearth, and home", "they're concerned with basic needs and simple pleasures and have little use for ostentation", "they cherish the bonds of family and friendship as well as the comforts of hearth and home, harboring few dreams of gold and glory", "they are generous, happily sharing what they have even in lean times", "halflings live in small, peaceful communities". This does not paint a portrait of a race that is predisposed to theft or trouble, though to be fair, the halfling write-up makes several references to being able to "avoid notice". Of course, "avoiding notice" also means, keeping your nose clean and staying out of trouble, not stealing things.
Gnomes: The gnome write-up also makes reference to being stealthy and avoiding notice, but, instead of emphasising how halflings try to avoid trouble, and care for their communities, it goes out of its way to point out the gnomish love of pranks and tricks.
11) Sorcerer
Elves: No mention.
Dwarves: No mention.
Halflings: No mention.
Gnomes: No mention.
12) Warlocks
Elves: No mention.
Dwarves: No mention.
Halflings: No mention.
Gnomes: No mention.
13) Wizards
Elves: "Elves love nature and magic", "their skill and magic allow them to support themselves without the need for clearing and plowing land", "Elves also enjoy exercising their magical prowess or gaining greater magical power"
Dwarves: No mention.
Halflings: No mention.
Gnomes: "their homes are well-hidden by both clever construction and simple illusions", "natural knack for illusion", "using illusions and trickery to conceal themselves",
Final tally: Dwarves' write-ups suggest 3 classes. Gnomes and Elves' write-ups suggest 5 classes that spring naturally from how they are described. Halflings have 1: bards. And even among bards, the elven write-up goes into more detail than the halfling write-up.