Professions are what the common folk of the realm do to provide for their families and promote the well-being of the community. Players can enjoy the benefits of these jobs themselves, slanting them towards their own adventuring needs of course. Players will likely be more interested in increasing the survivability of their character through a profession. Indeed, most of these professions will and some more so than others. There has been next to no effort to balance the professions during fight scenarios. Instead, the DM is advised to increase or vary the challenge of the fights so that players must rely on their professions to succeed. This fosters the idea that as skill and power increases so do the challenges the party can face.
It may be more helpful to think of the party having a certain effective challenge rating. Normally, this would increase with levels since as players level they become more powerful. As magical weapons and armor are introduced, the party can assume harder encounters than they could at the same level without the buffs. Professions add to the amount of a challenge the party can take on and survive. So professions can be seen as a way to move past easy stuff and focus on the things that require heroes of their caliber.
For example, an alchemist will likely have a plethora of healing potions. This increase in the functional health pool of the party can open up some new mechanics the DM can introduce to their fights. A lich can now pin a player to a wall for a turn with bone spears so that their buddies have to pull them off since everyone can now take an extra hit. When in an arena with a giant, if the fighter wants to take the giant head on they will need a strength potion so that they can directly parry the giant's blows. Otherwise, the party will have to find more clever means to tackle this adversary.
This expansion of DM options is much more apparent in RP situations. The professions can open up new adventures, seeking rare ingredients or secluded masters of the craft. Other practitioners can now be friend or foe. Challenging the conventions of the day in regards to their craft can be experimented with in their free time, opening up new mechanics and tools in the party's toolkit.