If you look at some of the art in this thread, you'll see that not every version of the imagery is cartoony.
Further there is nothing in their description that says they need to be silly ... in fact, although they as a race tend to be peaceful and seek harmonious responses to difficult situations, they're listed as being capable of being very threatening. I'd put them beneath halflings and dwarves on the scales of silliness.
From their race description:
- When provoked, firbolgs demonstrate formidable skills with weapons and druidic magic.
- If the settlers clearly display evil intentions, however, the firbolgs martial their strength and magic for a single overwhelming attack.
One Firbolg I saw that was clearly not silly and I definitely would not characterize as cartoony.
A Hexblade Warlock (and I think he had at least 1 level of fighter) that made a pact with a dark power of the Shadowfell to gain the power he needed to protect his people. They would not accept the deal he made and banished him into the world until he could sever his pact with this dark force. However, the dark force had him convinced that he could better serve his people by being a creature that stands between the darkness of the Shadowfell and the light of the Feywild (which was attuned to positive energy in the lore of the world - the anti-Shadowfell - and was the home of firbolgs in the setting lore). He wielded a huge sword granted by the dark power and blended warlock powers of darkness (Armor of Agathys, Hex) and light (Summon Fey Spirit, a homebrew summon swarm spell). I only saw him for a few sessions, but he was well roleplayed to be a soldier longing to be able to set down his weapons and return home, knowing that the home he left behind had turned its back on him due to the things he'd done to protect them. He was very effective in combat, as most well built Hexblades are. His charisma was only a 13, so he focused on spells that did not have saves or attack rolls. He was Strength based for his combat abilities.
Regardless, you're not required to use them, but I would argue there is a lot more open space around their description than you're seeing if you consider them inherently silly or cartoony.